Zoom lens

ABSTRACT

A high range zoom lens is disclosed, comprising, from front to rear, a first lens unit of positive refractive power, a second lens unit of negative refractive power, a third lens unit of positive or negative refractive power and a fourth lens unit of positive refractive power, the second and third lens units being movable for zooming, wherein an aspheric surface is introduced into the second or third lens unit at a specified location so that the variation of aberrations with zooming is as far reduced for high performance as possible.

BACKGROUND OF THE INVENTION

1. Field of the Invention:

This invention relates to zoom lenses and, more particularly, to zoomlenses using an aspheric surface in the lens system at an appropriatelocation to get as large a relative aperture as 1.7 in F-number for thewide-angle end with as high a zoom ratio as 10 to 25, while stillmaintaining good optical performance throughout the entire zoomingrange, and suited to television cameras, photographic cameras, or videocameras.

2. Description of the Related Art:

In the field of art of television cameras, photographic cameras, orvideo cameras, there has been a growing demand for zoom lenses of largerelative aperture and high range with good optical performance.

Of these, especially the color television camera for broadcasting has tobe quick and easy in handling and good in manageability, which areregarded as important. To meet such requirements, even the image pickupdevices in recent years are taking a smaller size of CCD (solid-stateimage sensor) such as 2/3, or 1/2 inch ones in the main stream.

This CCD has its resolution almost uniform over the entire area of theimage frame. To ensure that a zoom lens is usable with this CCD,therefore, the resolving power of the zoom lens must be uniform from thecentral to the marginal zone of the full aperture.

For this purpose, of all aberrations, for example, astigmatism,distortion and lateral chromatic aberration are necessarily subjected togood correction for high optical performance over the entire area of theimage frame. It is further desired that the zoom ratio is high, whilethe size and the weight are nonetheless small and light. In addition,the back focal distance is so long that a color separating system andvarious filters can be put in front of the image pickup device.

The zoom lens of the type comprising, from front to rear, a focusing orfirst lens unit of positive refractive power, a second lens unit ofnegative power for varying the focal length, a third lens unit ofpositive or negative refractive power for compensating for the imageshift with zooming and a fourth lens unit of positive refractive powerfor forming an image, or the so-called 4-unit zoom lens, has found itsuse in many color television cameras for broadcasting, since it iscomparatively easy to increase the zoom ratio and the relative aperture.

Of the 4-unit zoom lenses, a large relative aperture, high range one of1.6 to 1.8 in F-number whose range is 20 is proposed in, for example,Japanese Laid-Open Patent Applications No. Sho 54-127322 and No. Sho51-14034.

Given a zoom lens of large relative aperture (F-number: 1.6-1.8) andhigh range (zoom ratio: 10-40), to include high optical performance overthe entire zooming range, there is need to set forth proper design rulesfor the refractive power of each lens unit and for the construction andarrangement of the constituent lenses.

In general, to maintain good stability of aberration correction for thehigh optical performance throughout the entire zooming range, it becomesnecessary to increase the degree of freedom on the aberration correctionby, for example, increasing the number of lens elements in each lensunit.

For this reason, if it is attempted to get the large relative aperture,high range zoom lens, the total number of constituent lenses wouldunavoidably increase and a problem would arise in that the size of theentire system comes to increase largely.

In respect to the imaging performance, as one sees the central zone ofthe full aperture which gives best contrast to the image, or theso-called best image focus, variation of it with zooming comes to be aproblem. This is ascribable mainly to the variation of sphericalaberration with zooming.

The variation with zooming of spherical aberration in general is shownin FIG. 17, where letting the zoom ratio be denoted by Z and theshortest focal length by fw, the spherical aberration increases in theminus direction, or, its under-correction for the Gauss image planegrows, as zooming goes from the wide-angle end, where the sphericalaberration is zero, to a position for a focal length fw'=fw×Z^(1/4).After having left that zooming position, the amount of under-correctionstarts to decrease, reaching zero at a certain zooming position. Fromthis on, the spherical aberration now changes to over-correction.

The over-correction increases to a maximum at or near a zooming positionfor a focal length fd=ft×(F_(NO).w /F_(NO).t), where ft is the longestfocal length and F_(NO).w and F_(NO).t are the F-numbers at thewide-angle and telephoto ends, respectively. It is at this zoomingposition that the F-number starts to increase (the lens system getsdarker). In other words, the F drop begins from this position. Aszooming goes on, the amount of over-correction decreases, reachingalmost zero in the telephoto end.

Meanwhile, if the F-number in the telephoto end is greater by 5% orbelow than that in the wide-angle end, or, almost no F drop takes place,the zoom lens has its spherical aberration, as shown in FIG. 18, mostover-corrected just before the telephoto end, or at a zooming positionfor a focal length ft'=fw×Z^(3/4). On going past this zooming position,the amount of over-correction decreases. In the telephoto end, it tendsto change to slight under-correction.

So, if correction is otherwise made to bring the spherical aberration toalmost zero in the telephoto end, the over-correction in the zoomingposition for the focal length ft' even grows greater.

In such a manner, for the zoom lenses, particularly the one having thestart point of the F drop within the zooming range, the sphericalaberration in the telephoto end is very difficult to control. In theprior art, therefore, it has been the common practice to increase thenumber of constituent lenses in either of the lens unit for focusing andthe lens unit for varying the focal length in order to lessen thevariation of spherical aberration with zooming. For this reason, thereis a problem that the whole lens system increases in the bulk and sizeand becomes complicated in the structure of construction.

SUMMARY OF THE INVENTION:

The present invention in application to the so-called 4-unit zoom lenssets forth proper rules for the refractive power of every lens unit andfor the determination of the F-number. As the off-axial and on-axialrays of light travel throughout the lens surfaces, at least one lenssurface which satisfies certain conditions for the heights of incidenceof the rays of light thereon is selected to apply aspheric spherethereto. When these rules and conditions are satisfied at once, thevariation with zooming of spherical aberration is minimized and,particularly on the telephoto side, the spherical aberration iscorrected well. It is, therefore, an object of the invention to providea zoom lens having as large a relative aperture as about 1.7 in F-numberin the wide-angle end and as high a range as 10 to 25, while stillmaintaining high optical performance throughout the entire zoomingrange.

A zoom lens of the invention comprises, from front to rear, a first lensunit of positive refractive power which is stationary during zooming, asecond lens unit of negative refractive power for varying the focallength, a third lens unit of negative refractive power for compensatingfor the image shift with zooming, and a fixed fourth lens unit ofpositive refractive power, wherein the F-number of the entire systemstarts to increase at an arbitrary zooming position when zooming goesfrom the wide-angle end to the telephoto end, wherein the first lensunit has a focal length f16 and an F-number F_(NO).1, the second lensunit has a lateral magnification β2win the wide-angle end and has afocal length f2, and an axial light beam is incident on the last lenssurface in the second lens unit at a height h2m, wherein the second lensunit is constructed with at least four lens surfaces, and at least oneof the fourth and later lens surfaces of the second lens unit satisfying

    1.09<hm/ht . . .                                           (1-4)

where hm is the maximum height of incidence of the axial beam and ht isthe maximum height of incidence of the axial beam in the telephoto end,is an aspheric surface, and wherein, letting the F-number of the secondlens unit be denoted by F_(NO).2, the focal length and F-number of theentire system in the telephoto end by ft and F_(NO).t, respectively, andthe zoom ratio by Z, and putting

    F.sub.NO.1 =F1/(ft/F.sub.NO.t)

    F.sub.NO.2 =f2/(2×h2m)

the following conditions are satisfied:

    10<Z

    1.01<F.sub.NO.1 <1.65 . . .                                (1--1)

    0.65<F.sub.NO.2 <1.25 . . .                                (1-2)

    -0.40<β2w<-0.15 . . .                                 (1-3)

In particular, the aspheric surface described above, when applied to apositive refracting surface, is of such shape that the positiverefractive power gets progressively stronger toward the marginal zone ofthe full aperture, or when applied to a negative refracting surface, isof such shape that the negative refractive power gets progressivelyweaker toward the marginal zone. In either case, a characteristicfeature is that, letting the aspheric amounts at 1.0, 0.9 and 0.7 of theeffective lens diameter of the aspheric surface be denoted by Δ10, Δ9and Δ7, respectively, the following conditions are satisfied: ##EQU1##

Another zoom lens of the invention comprises, from front to rear, afirst lens unit of positive refractive power which is stationary duringzooming, a second lens unit of negative refractive power for varying thefocal length, a third lens unit of negative refractive power forcompensating for the image shift with zooming, and a fixed fourth lensunit of positive refractive power, wherein, letting the zoom ratio bedenoted by Z, the focal length and F-number of the first lens unit by f1and F_(NO).1, respectively, the lateral magnification in the wide-angleend of the second lens unit by β2w, the focal length of the second lensunit by f2, and the height of incidence of an axial light beam on thelast surface in the second lens unit by h2m, wherein the second lensunit is constructed with at least four lens surfaces, and one of thefourth and later lens surfaces in the second lens unit satisfying thefollowing condition:

    1.17<ht/hz . . .                                           (2-4)

where hz is the maximum height of incidence of the axial light beam in azooming position where the zoom ratio takes a value of Z^(3/4), and htis the maximum height of incidence of the axial light beam in thetelephoto end, is an aspheric surface, and wherein, letting the F-numberof the second lens unit be denoted by F_(NO).2, the focal length andF-number in the telephoto end and the F-number in the wide-angle end ofthe entire system by ft, F_(NO).t and F_(NO).w, respectively, andputting

    F.sub.NO.1 =f1/(ft/F.sub.NO.t)

    F.sub.NO.2 =f2/(2×h2m)

    F.sub.NO.R =F.sub.NO.t /F.sub.NO.w

the following conditions are satisfied:

    10<Z

    F.sub.NO.R <1.05

    1.01<F.sub.NO.1 <1.65 . . .                                (2-1)

    0.65<F.sub.NO.2 <1.28 . . .                                (2--2)

    -0.40<β2w<-0.16 . . .                                 (2-3)

In particular, the aspheric surface described above, when in applicationto a positive refracting surface, is of such shape that the positiverefractive power gets progressively weaker toward the marginal zone ofthe full aperture, or when in application to a negative refractingsurface, is of such shape that the negative refractive power getsprogressively stronger toward the marginal zone. A characteristicfeature is that, letting the aspheric amounts at 1.0, 0.9 and 0.7 of theeffective lens diameter of the aspheric surface be denoted by Δ10, Δ9and Δ7, respectively, the following conditions are satisfied: ##EQU2##

A further zoom lens of the invention comprises, from front to rear, afirst lens unit of positive refractive power which is stationary duringzooming, a second lens unit of negative refractive power for varying thefocal length, a third lens unit of positive refractive power forcompensating for the image shift with zooming and a fixed fourth lensunit of positive refractive power, wherein the entire system varies itsfocal length from the shortest one fw to the longest one ft in a zoomratio Z with the F-numbers F_(NO).w and F_(NO).t in the wide-angle andtelephoto ends, respectively, the first lens unit has a focal length f1and an F-number F_(NO).1, the second lens unit during zooming varies itsmagnifying power in a range including unity, the variation of itslateral magnification amounting to a range Z2, the third lens unitduring zooming varies its magnifying power in a range including unity,an axial light beam is incident on the third lens unit at a maximumheight h3m during zooming and at a maximum height h3T in the telephotoend, the third lens unit includes at least one cemented lens of whichmedia on the front and rear sides of the cemented surface differ in therefractive index from each other by an amount Δn3, and the third lensunit has a focal length F3 and an F-number F_(NO).3, the followingconditions being satisfied:

    1.25<F.sub.NO.1 <1.6 . . .                                 (3)

where

    F.sub.NO.1 =f1/(ft/F.sub.NO.t)

    5<Z2 . . .                                                 (4)

    0.2<Z2/Z<0.3 . . .                                         (5)

    0.8<F.sub.NO.3 <1.2 . . .                                  (6)

where

F_(NO).3 =f3 (2×h3m)

    0.17<Δn3 . . .                                       (7)

and wherein an aspheric surface is applied to at least one of lenssurfaces in the third lens unit which satisfies the following condition:

    1.15<h3m/h3· . . .                                (8)

In particular, the aspheric surface described above is of such shapethat the positive refractive power gets progressively stronger towardthe-marginal zone of the full aperture, satisfying the followingconditions:

    0<ΔX.sub.7 /f3<4×10.sup.-5

    9×10.sup.-6 <ΔX.sub.9 /f3<3×10.sup.-4

    3×10.sup.-5 <ΔX.sub.10 /f3<6×10.sup.-4

where ΔX₁₀, ΔX₉ and ΔX₇ are the aspheric amounts at 1.0 0.9 and 0.7 ofthe effective lens diameter of the aspheric surface, respectively.

A furthermore feature of the invention as applied to the zoom lenscomprising, from front to rear, a focusing system, a zooming system anda relay system is that, letting the shortest and longest focal lengthsbe denoted by fw and ft, respectively, the zoom ratio by Z, an asphericsurface is applied to at least one lens surface on which a ray of lightcoming from the maximum angle of field of view is incident at a heighthW in the wide-angle end and at a height hM in a zooming position wherethe focal length takes a value of fM=fW×Z^(1/4), and the highest of therays of the axial light beam is incident at a height hT in the telephotoend, the aforesaid lens surface satisfying the following condition:

    1.2<hW/hM, and hT<hW . . .                                 (9)

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a lens block diagram of a numerical example 1 of theinvention.

FIG. 2 is a lens block diagram of a numerical example 2 of theinvention.

FIG. 3 is a lens block diagram of a numerical example 3 of theinvention.

FIG. 4 is a lens block diagram of a numerical example 4 of theinvention.

FIG. 5 is a lens block diagram of a numerical example 5 of theinvention.

FIG. 6 is a lens block diagram of a numerical example 6 of theinvention.

FIG. 7 is a lens block diagram of a numerical example 7 of theinvention.

FIG. 8 is a lens block diagram of a numerical example 8 of theinvention.

FIGS. 9(A) to 9(E) are aberration curves of the numerical example 1.

FIGS. 10(A) to 10(E) are aberration curves of the numerical example 2.

FIGS. 11(A) to 11(E) are aberration curves of the numerical example 3.

FIGS. 12(A) to 12(E) are aberration curves of the numerical example 4.

FIGS. 13(A) to 13(E) are aberration curves of the numerical example 5.

FIGS. 14(A) to 14(E) are aberration curves of the numerical example 6.

FIGS. 15(A) to 15(E) are aberration curves of the numerical example 7.

FIGS. 16(A) to 16(E) are aberration curves of the numerical example 8.

FIG. 17 is a diagram used to explain the variation of aberration of thezoom lens with zooming.

FIG. 18 is a diagram used to explain the variation of aberration of thezoom lens with zooming.

FIG. 19 is a diagram used to explain the variation of aberration of thezoom lens with zooming.

FIGS. 20 (A) to 20 (C) are diagrams showing the optical paths in theoperative positions of the zoom lens.

FIGS. 21 (A) to 21 (C) are diagrams showing the optical paths in theoperative positions of the zoom lens.

FIG. 22 is a lens block diagram of a numerical example 9 of theinvention.

FIG. 23 is a lens block diagram of a numerical example 10 of theinvention.

FIG. 24 is a lens block diagram of a numerical example 11 of theinvention.

FIGS. 25(A) to 25(E) are aberration curves of the numerical example 9.

FIGS. 26(A) to 26(E) are aberration curves of the numerical example 10.

FIGS. 27(A) to 27(E) are aberration curves of the numerical example 11.

FIG. 28 is a diagram used to explain the variation of aberration of thezoom lens with zooming.

FIG. 29 is a diagram used to explain the variation of aberration of thezoom lens with zooming.

FIGS. 30 (A) to 30 (C) are diagrams showing the optical paths in theoperative positions of the zoom lens.

FIG. 31 is a lens block diagram of a numerical example 12 of theinvention.

FIGS. 32(A) to 32(E) are aberration curves of the numerical example 12.

FIGS. 33(A) and 33(B) are diagram used to explain the variation ofoff-axial aberration of the conventional zoom lens with zooming.

FIGS. 34(A) and 34(B) are diagram used to explain the variation ofoff-axial aberration of the zoom lens of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIGS. 1 to 8 in block diagrams show the numerical examples 1 to 8 ofzoom lenses of the invention in the wide-angle end.

The first four examples 1-4 show a case where the zoom lens starts toincrease in the F-number (to become slower in the speed) at a certainzooming position during zooming from the wide-angle end to the telephotoend, or, an F drop occurs.

The next three examples 5-8 constitute another case where the amount bywhich the F-number in the telephoto end, is larger than that in thewide-angle end is not more than 5%, or, almost no F drop occurs.

In FIGS. 1-8, F denotes a first lens unit of positive refractive power,or a focusing lens unit (or front lens members).

V denotes a second lens unit for varying the focal length, or a variatorof negative refractive power. As it moves axially toward the image sidemonotonously, the focal length varies from the shortest to the longestone. A compensator C of negative refractive power moves axiallynon-linearly in a locus convex toward the object side to compensate forthe shift of an image plane with zooming. The variator V and thecompensator C constitute a zooming system.

SP (R19) stands for a stop, and R stands for a relay lens unit ofpositive refractive power as the fixed fourth lens unit. P denotes acolor separation prism and optical filters shown in FIGS. 1-8 as a glassblock.

To realize a zoom lens whose zoom ratio Z is 10 or higher, while stillpermitting great increase of the aperture ratio throughout the zoomingrange, the invention is, for a start, to make use of what is so fast asto satisfy the before-stated condition (1-1) or (2-1) in the front lensunit F. By this, the great increase of the aperture ratio of the entirelens system is achieved in such a manner that the spherical aberrationis well corrected in the telephoto end.

When the lower limit of the condition (1-1) or (2-1) is exceeded, itbecomes difficult to well correct spherical aberration in the telephotoend. When the upper limit is exceeded, it becomes difficult to get themuch desired increase of the aperture ratio.

The variator V is also made so as to satisfy the before-stated condition(1-2) or (2-2) for the F-number. By this, similarly to the condition(1-1) or (2-1), spherical aberration is well corrected in the telephotoend to make it easy to greatly increase the aperture ratio of the entirelens system.

When the lower limit of the condition (1-2) or (2-2) is exceeded, goodcorrection spherical aberration in the telephoto end becomes difficultto perform likewise as with the condition (1-1) or (2-1). When the upperlimit is exceeded, it becomes difficult to get the great increase of theaperture ratio.

Further, as regards the lateral magnification, the variator V is madealso to satisfy the before-stated condition (1-3) or (2-3). This assureshold of the zoom ratio at a predetermined value, when the variation ofaberrations is reduced for improvement of the optical performance overthe entire zooming range.

When the lower limit of the condition (1-3) or (2-3) is exceeded, itbecomes difficult to greatly increase the zoom ratio. When the upperlimit is exceeded, it becomes difficult to reduce the variation ofaberrations over the entire zooming range and, therefore, to obtain highoptical performance.

Thus, for the zoom lenses shown in FIG. 1 to FIG. 8, good stability ofaberration correction is maintained for high optical performancethroughout the entire zooming range, when all the conditions mentionedabove are satisfied.

Next, an explanation is given to the features of the F-drop-behaved zoomlenses shown in FIG. 1 to FIG. 4.

With the zoom lens of F drop behavior, as shown in FIGS. 20(A) to 20(C),the height of incidence of an axial light beam on the variator Vgradually increases as zooming goes from the wide-angle end to thetelephoto end, reaching a maximum at a start point of the F drop(zooming position fd shown in FIG. 20(B)). Because of the F drop, theheight then becomes lower in the telephoto end than that.

The height of incidence of the axial light beam on the front lens unit F(first lens unit) gradually increases with zooming from the wide-angleend to the position for the start of the F drop and remains constantfrom that position to the telephoto end.

It is to be noted that FIGS. 20(A) to 20(C) show part of the opticalsystem of FIG. 1 (or a fragmentary optical system of from the first lensunit to the third lens unit) with the rays of light in each operativeposition.

In the present embodiment, as far as the use of the front lens unit incorrecting spherical aberration is concerned, the correction mainly forthe telephoto end is preponderantly done. At or near the zoomingposition fd for start of the F drop, therefore, under-correctionresults. With the variator V in turn, the negative refractive power ismade strengthened to achieve the increase of the zoom ratio with thelimitation of the size of the entire lens system to a minimum.

For this reason, as zooming approaches the position for the start of theF drop at which the height of the axial light beam from the optical axisbecomes high, over-corrected spherical aberrations of higher order areproduced.

To take a counter-measure, it is considered that there is some lenssurface in the variator on which the height of incidence of the axiallight beam can reach the highest value hm at the start point of the Fdrop and, because of the presence of the F drop, lowers to a value ht inthe telephoto end. In the practical examples of F-drop-behaved zoomlenses shown in FIGS. 1 to 4, therefore, at least one lens surface thathas its ratio of the height hm to the height ht satisfying the followingcondition:

    1.09<hm/ht . . .                                           (1-4)

is selected to be used for application of an aspheric sphere thereto. Bythis, the spherical aberrations of higher order which would be otherwiseover-corrected only when zooming in a region around the start point ofthe F drop are well corrected, since such an effect is almost lost inthe other regions.

Particularly in the present embodiment, to selectively well correct thespherical aberrations of higher order, the before-described condition(1-5) for determination of the shape of the aspheric surface is setforth. This means that the aspheric surface is almost completelyspherical in the central zone and the aspheric nature gets rapidlygreater toward the margin.

It should be pointed out that the condition mentioned above is given tothe zooming system of the zoom lens so that the aspheric surface takeseffect only in that minor region of the zooming range which lies aroundthe start point of the F drop, and gives as little influence tospherical aberration and astigmatism as possible in the other regions ofthe zooming range.

Concretely speaking, of a plurality of lens surfaces constituting thevariator, the first three ones, when counted from the object side, havea large influence on the off-axial light beam in the wide-angle end. Tomake the astigmatism and distortion for the wide-angle end leaving notinfluenced, the aspheric sphere is applied to the fourth or later lenssurface.

That, in the condition (1-4), the ratio of the heights hm and htapproaches 1 implies that zooming from the neighborhood of the startpoint of the F drop to the telephoto end causes little change of theheight of incidence of the axial ray on the aspheric surface. The use ofthe aspheric surface at such a location leads to produce the effect ofcorrecting spherical aberration not only when zoomed in the neighborhoodof the start point of the F drop, but also to extend the influence up tothe telephoto end in respect to spherical aberration.

In other words, if the spherical aberration is corrected by thataspheric surface to the under direction in the zooming position for thefocal length fd (=(F_(NO).w /F_(NO).t)×ft), the spherical aberration inthe telephoto end, too, is subject to the influence of this asphericsurface, being brought to a change in the under direction. Thus, theeffect of correcting the variation of spherical aberration is weakened.So, it should be avoided.

It will be appreciated that in the present embodiment, the lens surfaceto which the aspheric sphere is to be applied is properly chosen tominimize the influence on the spherical aberration in the telephoto end.Hence, as shown in FIG. 19, the spherical aberration in the neighborhoodof the F drop is corrected so as to effect a shift from a curve (dashedline) 51a to another one (solid line) 51b. Thus, good stability ofspherical aberration correction is maintained throughout the entirezooming range.

Next, an explanation is given to the features of those zoom lenses shownin FIGS. 5 to 8 whose F-number in the telephoto end increases from thatin the wide-angle end to not more than 5%, or which has almost no F dropover the entire zooming range.

In the zoom lenses shown in FIG. 5 to FIG. 8, the height of incidence ofthe axial light beam on the variator V gradually increases with zoomingfrom the wide-angle end to the telephoto end as shown in FIGS. 21(A) to21(C), reaching the highest at or near the telephoto end (FIG. 21(C)).Likewise with this, even for the front lens unit F, the highest heighttakes place at or near the telephoto end.

It is to be noted that FIGS. 21(A) to 21(c) show part of the opticalsystem of FIG. 5 (or an optical system of from the first to the thirdlens unit) with the optical paths in the three operative positions.

As zooming begins at the wide-angle end, when a zooming position for azoom ratio of Z^(3/4) or a focal length ft' (=fw×Z^(3/4)) (FIG. 21 (B))is reached, the ray of maximum diameter of the axial beam is incident onthe front lens unit F, the variator V and the compensator C atrespective heights nearly equal to 1/2 of the full aperture. For suchheights of incidence, spherical aberration correction has to be carriedout in difficult situation, since the variator V has a strong refractivepower. Under the influence of such a variator, over-corrected sphericalaberration is apt to be produced. To correct this, measures are adoptedwithin the front lens unit F to produce somewhat under-correctedspherical aberration.

Then, when zoomed to the telephoto end, the spherical aberration becomeseven more under-corrected, because the ray of maximum diameter of theaxial beam passes through the front lens unit F at higher heights.

To take a counter-measure, the variator V may otherwise producespherical aberrations of higher order. In this case, however,under-corrected spherical aberrations of higher order are left arisingentirely.

In the practical examples of zoom lenses shown in FIGS. 5 to 8,therefore, an aspheric sphere is applied to one of the lens surfacesconstituting the variator so as to correct the under-corrected sphericalaberrations of higher order effectively in only the zooming region nearthe telephoto end, but not very effectively in the other zooming region,particularly at the zooming position for a zoom ratio of Z^(3/4) or afocal length of fw×Z^(3/4).

In particular, as the ray of maximum diameter of the axial beam travelsthrough the variator V at a height hz when in the zooming position forfw×Z^(3/4) or at a height ht when in the telephoto end, an asphericsphere is applied to at least one of lens surfaces which satisfies thefollowing condition:

    1.17<ht/hz . . .                                           (2-4)

By this, over-corrected spherical aberrations of higher order areproduced to effect correction entirely in good balance.

Particularly in the present embodiment, the shape of the asphericsurface is determined to well correct the residual under-correctedspherical aberrations of higher order. For this purpose, the condition(2-5) described before is set forth. When this condition is satisfied,the central zone of the aspheric surface is almost spherical, and thenearer to the margin, the greater the aspheric sphere becomes.

It should be noted that the aforesaid condition is assigned to thezooming system of the zoom lens, so that the aspheric surface brings itseffect into full play in only that region of the entire zooming rangewhich lies at or near the telephoto end, and gives as little influenceto spherical aberration and astigmatism as possible in the other zoomingregions.

Concretely speaking, of a plurality of lens surfaces constituting thevariator V, the first three ones, when counted from the object side,have a great influence on the off-axial light beam in the wide-angleend. To avert influences on astigmatism and distortion in the wide-angleend, therefore, the aspheric sphere is applied to the fourth or laterlens surface.

When the condition (2-4) is violated, as this means that the ratio ofthe heights hz and ht is nearer to 1, and, therefore, that the height ofincidence of the axial light beam changes to small extent as zoominggoes from the position for fw×Z^(3/4) to the telephoto end, the asphericsurface has the effect of correcting spherical aberration not only at ornear the telephoto end, but also gives the influence up to the sphericalaberration in the zooming position for fw×Z^(3/4).

This leads to an objectionable result that if the spherical aberrationat or near the telephoto end is corrected in the over direction by theaspheric surface, even the spherical aberration at or near the zoomingposition for fw×Z^(3/4) is influenced by the aspheric surface to changein the over direction. Thus, the effect of correcting the variation ofspherical aberration is weakened.

It will be appreciated that in the present embodiment, the lens surfaceto which the aspheric surface is to be applied is properly selected sothat, while giving little influence to the spherical aberration in thezooming position for fw×Z^(3/4) the spherical aberration in theneighborhood of the telephoto end is corrected as shown in FIG. 19 insuch a way as to shift from a curve 51c (dot-and-dash line) to a curve51b (solid line). Thus, good stability of spherical aberrationcorrection is maintained throughout the entire zooming range.

The features of each of the practical examples (numerical examples) ofthe invention are described below.

The numerical example 1 shown in FIG. 1 has a zoom ratio of 13. A frontlens unit F of from R1 to R8 for focusing has a positive refractivepower. A variator V of from R9 to R15 moves toward the image sidemonotonously to effect variation of the focal length from the wide-angleend to the telephoto end. A compensator C of from R16 to R18 functionsto compensate for the shift of an image plane with zooming and has anegative refractive power. When zooming from the wide-angle end to thetelephoto end, the compensator C moves while depicting an arcuate locusconvex toward the object side. SP (R19) stands for a stop. A relay lensunit R of from R20 to R37 has the image forming function. R38 and R39define an equivalent glass block to a color separation prism.

In this numerical example 1, as an indicator of increase of the apertureratio, the F-number F_(NO).1 of the front lens unit F is defined byF_(NO).1 =f1/(ft/F_(NO).t). Then, F_(NO).1 =1.08. With this value ofF-number of the front lens unit F when sustained over the entire zoomingrange, as the F-number F_(NO).2 of the variator V is defined by F_(NO).2=f2/(2×h2m), it gives as large an aperture ratio as F_(NO).2 =0.89.

For these large values of the aperture ratio, the front lens unit F isconstructed with four lenses of minus-plus-plus-plus power arrangementin this order from the object side. By the negative lens, sphericalaberration is diverged, thus permitting the front lens unit F tosuppress the spherical aberration from increasing in itself. Thevariator V is constructed with four lenses of minus-minus-minus-pluspower arrangement in this order from the object side. By the positivelens, spherical aberration is converted, thus causing the variator V tosuppress the spherical aberration from increasing in itself.

The lateral magnification β2w for the wide-angle end of the variator Vis, because of the zoom ratio being 13, taken somewhat large in theabsolute sense at β2w=-0.381.

The aspheric sphere is applied to the surface R15 and the condition(1-4) has its factor getting a value of hm/ht=1.10. The aspheric surfaceis so oriented that the positive refractive power gets stronger as theheight of the axial light beam increases. To correct sphericalaberration with good efficiency even in up to higher terms, the asphericcoefficients D and E only are in use, so that chief aberrationcorrection is made on spherical aberration. Such an aspheric surfacedeviates 1.05 μm at the highest height of incidence of the axial lightbeam.

The spherical aberration, astigmatism and distortion of the numericalexample 1 in five zooming positions are shown in FIGS. 9(A) to 9(E),respectively.

The numerical example 2 shown in FIG. 2 has a zoom ratio of 14. A frontlens unit F for focusing has a positive refractive power with R1 to R8.A variator V of R9 to R15 moves toward the image side monotonously tovary the focal length from the wide-angle end to the telephoto end. Acompensator C has a negative refractive power with R16 to R18. Tocompensate for the image shift with zooming, the compensator C movesaxially while depicting an arcuate locus convex toward the object side,as zooming goes from the wide-angle end to the telephoto end. SP (R19)stands for a stop. A relay lens unit R of R20 to R37 has the imageforming function. R38 and R39 define a glass block equivalent to a colorseparation prism.

In this numerical example 2, as an indicator of increase of the apertureratio, the F-number F_(NO).1 of the front lens unit F is defined byF_(NO).1 =f1/(ft×F_(NO).t). Then, F_(NO).1 =1.06. With this value ofF-number of the front lens unit F when sustained over the entire zoomingrange, as the F-number F_(NO).2 of the variator V is defined by F_(NO).2=f2/(2×h2m), it gives as large an aperture ratio as F_(NO).2 =0.679.

For these large values of the aperture ratio, the front lens unit F isconstructed with four lenses of minus-plus-plus-plus power arrangementin this order from the object side. By the negative lens, sphericalaberration is diverged, permitting the front lens unit F to suppress thespherical aberration from increasing in itself. The variator V isconstructed with four lenses of minus-minus-minus-plus power arrangementin this order from the object side. By the positive lens, the sphericalaberration is converged, thus causing the variator V to suppress thespherical aberration from increasing in itself.

The lateral magnification β2w for the wide-angle end of the variator Vis, because of the zoom ratio being 14, is taken somewhat large in theabsolute sense at β2w=-0.273.

The aspheric sphere is applied to the surface R13 and the condition(1-4) has its factor getting hm/ht=1.09. The aspheric surface is sooriented that the negative refractive power gets progressively weaker asthe height of incidence of the axial light beam increases. To correctspherical aberration with good efficiency even in up to higher terms,the aspheric coefficients D and E only are in use, so that chiefaberration correction is made on spherical aberration. Such an asphericsurface deviates 10.0 μm at the highest height of incidence of the axiallight beam.

The spherical aberration, astigmatism and distortion of the numericalexample 2 in five zooming positions are shown in FIGS. 10(A) to 10(E),respectively.

The numerical example 3 shown in FIG. 3 has a zoom ratio of 25. A frontlens unit F for focusing has a positive refractive power with R1 to R8.A variator V of R9 to R15 moves toward the image side monotonously tovary the focal length from the wide-angle end to the telephoto end. Acompensator C of R16 to R18 has a negative power. To compensate for theimage shift with zooming, the compensator C moves while depicting alocus convex toward the object side, as zooming goes from the wide-angleend to the telephoto end. SP (R19) stands for a stop. A relay lens unitR of R20 to R36 has the image forming function. R37 and R38 define aglass block equivalent to a color separation prism.

In this numerical example 3, as an indicator of increase of the apertureratio, the F-number F_(NO).1 of the front lens unit F is defined byF_(NO).1 =f1/(ft/F_(NO).t). Then, F_(NO).1 =1.6. With this value of theF-number of the front lens unit F when sustained over the entire zoomingrange, as the F-number F_(NO).2 of the variator V is defined by F_(NO).2=f2/(2×h2m), it gives as large an aperture ratio as F_(NO).2 =0.868.

For these large values of the aperture ratio, the front lens unit F isconstructed with four lenses of minus-plus-plus-plus power arrangementin this order from the object side. By the negative lens, sphericalaberration is diverged, permitting the front lens unit F to suppress thespherical aberration from increasing in itself. The variator V isconstructed with four lenses of minus-minus-minus-plus power arrangementin this order from the object side. By the positive lens, the sphericalaberration is converted, causing the variator V to suppress thespherical aberration from increasing in itself.

The lateral magnification β2w for the wide-angle end of the variator Vis, because of the zoom ratio being so large as 25, taken somewhat smallin the absolute sense at β2w=-0.163.

The aspheric sphere is applied to the surface R12 and the condition(1-4) has its factor getting hm/ht=1.19. The aspheric surface is sooriented that the positive refractive power gets stronger as the heightof incidence of the axial beam increases. To correct sphericalaberration with good efficiency even in up to higher terms, the asphericcoefficients C and D only are in use, so that chief aberrationcorrection is made on spherical aberration. Such an aspheric surfacedeviates 9.55 μm at the highest height of incidence of the axial lightbeam.

The spherical aberration, astigmatism and distortion of the numericalexample 3 in five zooming positions are shown in FIGS. 11(A) to 11(E),respectively.

The numerical example 4 shown in FIG. 4 has a zoom ratio of 25. A frontlens unit F for focusing has a positive refractive power with R1 to R8.A variator V of R9 to R15 moves toward the image side monotonously tovary the focal length from the wide-angle end to the telephoto end. Acompensator C of R16 to R18 has a negative refractive power. Tocompensate for the image shift with zooming, the compensator C movesaxially while depicting a locus convex toward the object side as zoominggoes from the wide-angle end to the telephoto end. SP(R19) stands for astop. A relay lens unit R of R20 to R36 has the image forming function.R37 and R38 define a glass block equivalent to a color separation prism.

In this numerical example 4, as an indicator of increase of the apertureratio, the F-number F_(NO).1 of the front lens unit F is defined byF_(NO).1 =f1/(ft/F_(NO).t). Then, F_(NO).1 =1.6. With this value of theF-number of the front lens unit F when sustained over the entire zoomingrange, as the F-number F_(NO).2 of the variator V is defined by F_(NO).2=f2/(2×h2m), it gives as large an aperture ratio as F_(NO).2 =1.21.

For these large values of the aperture ratio, the front lens unit F isconstructed with four lenses of minus-plus-plus-plus power arrangementin this order from the object side. By the negative lens, sphericalaberration is diverged, permitting the front lens unit F to suppress thespherical aberration from increasing in itself. The variator V isconstructed with four lenses of minus-minus-minus-plus power arrangementin this order from the object side. By the positive lens, the sphericalaberration is converged, causing the variator V to suppress thespherical aberration from increasing in itself.

The lateral magnification β2w for the wide-angle end of the variator Vis, because of the zoom ratio being so large as 25, taken somewhat smallin the absolute sense at β2w=-0.23.

The aspheric sphere is applied to the surface R15 and the condition(1-4) has its factor getting hm/ht=1.24. The aspheric surface is sooriented that the positive refractive power gets progressively strongeras the height of incidence of the axial beam increases. To correctspherical aberration with good efficiency even in up to higher terms,the aspheric coefficients D and E only are in use, so that chiefaberration correction is made on spherical aberration. Such an asphericsurface deviates 1.08 μm at the highest height of incidence of the axiallight beam.

The spherical aberration, astigmatism and distortion of the numericalexample 4 in five zooming positions are shown in FIGS. 12(A) to 12(E),respectively.

The numerical example 5 shown in FIG. 5 has a zoom ratio of 11. A frontlens unit F for focusing has a positive refractive power with R1 to R8.A variator V of R9 to R15 moves toward the image side monotonously tovary the focal length from the wide-angle end to the telephoto end. Acompensator C of R16 to R18 has a negative refractive power. Tocompensate for the image shift with zooming, the compensator C movesaxially while depicting a locus convex toward the object side as zoominggoes from the wide-angle end to the telephoto end. SP (R19) stands for astop. A relay lens unit R of R20 to R37 has the image forming function.R38 and R39 define a glass block equivalent to a color separation prism.

In the numerical example 5, as an indicator of increase of the apertureratio, the F-number F_(NO).1 of the front lens unit F is defined byF_(NO).1 =f1/(ft/F_(NO).t). Then, F_(NO).1 =1.06. With this value of theF-number of the front lens unit F when sustained over the entire zoomingrange, as the F-number F_(NO).2 of the variator V is defined by F_(NO).2=f2/(2×h2m), it gives as large an aperture ratio as F_(NO).2 =0.882.

For these large values of the aperture ratio, the front lens unit F isconstructed with four lenses of minus-plus-plus-plus power arrangementin this order from the object side. By the negative lens, sphericalaberration is diverged, permitting the front lens unit F to suppress thespherical aberration from increasing in itself. The variator isconstructed with four lenses of minus-minus-minus-plus power arrangementin this order from the object side. By the positive lens, the sphericalaberration is converged, causing the variator V to suppress thespherical aberration from increasing in itself.

The lateral magnification β2w for the wide-angle end of the variator Vis, because of the zoom ratio being 11, taken somewhat large in theabsolute sense at β2w=-0.381.

The aspheric sphere is applied to the surface R15 and the condition(2-4) has its factor getting ht/hz=1.24. The aspheric surface is sooriented that the positive refractive power gets progressively weaker asthe height of incidence of the axial beam increases. To correctspherical aberration with good efficiency even in up to higher terms,the aspheric coefficients D and E only are in use, so that chiefaberration correction is made on spherical aberration. Such an asphericsurface deviates 1.07 μm at the highest height of incidence of the axiallight beam.

The spherical aberration, astigmatism and distortion of the numericalexample 5 in five zooming positions are shown in FIGS. 13(A) to 13(E),respectively.

The numerical example 6 shown in FIG. 6 has a zoom ratio of 11. A frontlens unit F for focusing has a positive refractive power with R1 to R8.A variator V of R9 to R15 moves toward the image side monotonously tovary the focal length from the wide-angle end to the telephoto end. Acompensator C of R16 to R18 has a negative refractive power. Tocompensate for the image shift with zooming, the compensator C movesaxially while depicting a locus convex toward the object side as zoominggoes from the wide-angle end to the telephoto end. SP(R19) stands for astop. A relay lens unit R of R20 to R37 has the image forming function.R38 and R39 define a glass block equivalent to a color separation prism.

In this numerical example 6, as an indicator of increase of the apertureratio, the F-number F_(NO).1 of the front lens unit F is defined byF_(NO).1 =f1/(ft/F_(NO).t). Then, F_(NO).1 =1.05. With this value ofF-number of the front lens unit F when sustained over the entire zoomingrange, as the F-number F_(NO).2 of the variator V is defined by F_(NO).2=f2/(2×h2m), it gives as large an aperture ratio as F_(NO).2 =0.68.

For these large values of the aperture ratio, the front lens unit F isconstructed with four lenses of minus-plus-plus-plus power arrangementin this order from the object side. By the negative lens, sphericalaberration is diverged, permitting the front lens unit F to suppress thespherical aberration from increasing in itself. The variator V isconstructed with four lenses of minus-minus-minus-plus power arrangementin this order from the object side. By the positive lens, the sphericalaberration is converged, causing the variator V to suppress thespherical aberration from increasing in itself.

The lateral magnification β2w for the wide-angle end of the variator Vis, because of the zoom ratio being 11, taken somewhat large in theabsolute sense at β2w=-0.279.

The aspheric sphere is applied to the surface R13 and the condition(2-4) has its factor getting ht/hz=1.24. The aspheric surface is sooriented that the negative refractive power gets progressively strongeras the height of incidence of the axial light beam increases. To correctspherical aberration with good efficiency even in up to higher terms,the aspheric coefficients D and E only are in use, so that chiefaberration correction is made on spherical aberration. Such an asphericsurface deviates 9.17 μm at the highest height of incidence of the axiallight beam.

The spherical aberration, astigmatism and distortion of the numericalexample 6 in five zooming positions are shown in FIGS. 14(A) to 14(E),respectively.

The numerical example 7 shown in FIG. 7 has a zoom ratio of 17. A frontlens unit F for focusing has a positive refractive power with R1 to R8.A variator V of R9 to R15 moves toward the image side monotonously tovary the focal length from the wide-angle end to the telephoto end. Acompensator C of R16 to R18 has a negative refractive power. Tocompensate for the image shift with zooming, the compensator C movesaxially while depicting a locus convex toward the object side as zoominggoes from the wide-angle end to the telephoto end. SP (R19) stands for astop. A relay lens unit R of R20 to R36 has the image forming function.R37 and R38 define a glass block equivalent to a color separation prism.

In the numerical example 7, as an indicator of increase of the apertureratio, the F-number F_(NO).1 of the front lens unit F is defined byF_(NO).1 =f1/(ft/F_(NO).t). Then, F_(NO).1 =1.59. With this value ofF-number of the front lens unit F when sustained over the entire zoomingrange, as the F-number F_(NO).2 of the variator V is defined by F_(NO).2=f2/(2×h2m), it gives as large an aperture ratio as F_(NO).2 =0.906.

For these large values of the aperture ratio, the front lens unit F isconstructed with four lens units of minus-plus-plus-plus powerarrangement in this order from the object side. By the negative lens,spherical aberration is diverged, permitting the front lens unit F tosuppress the spherical aberration from increasing in itself. Thevariator V is constructed with four lenses of minus-minus-minus-pluspower arrangement in this order from the object side. By the positivelens, the spherical aberration is converged, causing the variator V tosuppress the spherical aberration from increasing in itself.

The lateral magnification β2w for the wide-angle end of the variator Vis, because of the zoom ratio being rather as large as 17, takensomewhat small in the absolute sense at β2w=-0.169.

The aspheric sphere is applied to the surface R12 and the condition(2-4) has its factor getting ht/hz=1.26. The aspheric surface is sooriented that the negative refractive power gets progressively strongeras the height of incidence of the axial light beam increases. To correctspherical aberration with good efficiency even in up to higher terms,the aspheric coefficients D and E only are in use, so that chiefaberration correction is made on spherical aberration. Such an asphericsurface deviates 9.35 μm at the highest height of incidence of the axiallight beam.

The spherical aberration, astigmatism and distortion of the numericalexample 7 in five zooming positions are shown in FIGS. 15(A) to 15(E),respectively.

The numerical example 8 shown in FIG. 8 has a zoom ratio of 17. A frontlens unit F for focusing has a positive refractive power with R1 to R8.A variator V of R9 to R15 moves toward the image side monotonously tovary the focal length from the wide-angle end to the telephoto end. Acompensator C of R16 to R18 has a negative refractive power. Tocompensate for the image shift with zooming, the compensator C movesaxially while depicting a locus convex toward the object side as zoominggoes from the wide-angle end to the telephoto end. SP (R19) stands for astop. A relay lens unit R of R20 to R36 has the image forming function.R37 and R38 define a glass block equivalent to a color separation prism.

In the numerical example 8, as an indicator of increase of the apertureratio, the F-number F_(NO).1 of the front lens-unit F is defined byF_(NO).1 =f1/(ft/F_(NO).t). Then, F_(NO).1 =1.59. With this value ofF-number of the front lens unit F When sustained over the entire zoomingrange, as the F-number F_(NO).2 of the variator V is defined by F_(NO).2=f2/(2×h2m), it gives as large an aperture ratio as F_(NO).2 =1.22.

For these large values of the aperture ratio, the front lens unit F isconstructed with four lenses of minus-plus-plus-plus power arrangementin this order from the front. By the negative lens, spherical aberrationis diverged, permitting the front lens unit F to suppress the sphericalaberration from increasing in itself. The variator V is constructed withfour lenses of minus-minus-minus-plus power arrangement in this orderfrom the object side. By the positive lens, the spherical aberration isconverged, causing the variator V to suppress the spherical aberrationfrom increasing in itself.

The lateral magnification β2w for the wide-angle end of the variator Vis, because of the zoom ratio being rather as large as 17, takensomewhat small in the absolute sense at β2w=-0.215.

The aspheric sphere is applied to the surface R15 and the condition(2-4) has its factor getting ht/hz=1.226. The aspheric surface is sooriented that the positive refractive power gets progressively weaker asthe height of incidence of the axial light beam increases. To correctspherical aberration with good efficiency even in up to higher terms,the aspheric coefficients D and E only are in use, so that chiefaberration correction is made on spherical aberration. Such an asphericsurface deviates 1.08 μm at the highest height of incidence of the axiallight beam.

The spherical aberration, astigmatism and distortion of the numericalexample 8 in five zooming positions are shown in FIGS. 16(A) to 16(E),respectively.

Next, the numerical data for the above-mentioned examples 1 to 8 of theinvention are shown, where Ri is the radius of curvature of the i-thlens surface when counted from the object side, Di is the i-th axiallens thickness or air separation when counted from the object side, andNi and νi are respectively the refractive index and Abbe number of theglass of the i-th lens element when counted from the object side.

The shape of the aspheric surface is expressed in the coordinates withan X axis in the axial direction and an H axis in the directionperpendicular to the optical axis, the direction in which light advancesbeing taken as positive, by the following equation: ##EQU3## where R isthe radius of the osculating sphere, and A, B, C, D and E are theaspheric coefficients.

    ______________________________________                                        Numerical Example 1                                                           f = 9.5-123.5 Fno = 1:1.7-2.05 2ω = 60.1°-5.10°           ______________________________________                                        R1 = 1325.19                                                                             D1 = 2.50   N1 = 1.81265                                                                              ν1 = 25.4                               R2 = 106.20                                                                              D2 = 3.74                                                          R3 = 202.27                                                                              D3 = 9.23   N2 = 1.43496                                                                              ν2 = 95.1                               R4 = -140.90                                                                             D4 = 0.15                                                          R5 = 79.68 D5 = 10.83  N3 = 1.49845                                                                              ν3 = 81.6                               R6 = -208.30                                                                             D6 = 0.15                                                          R7 = 49.78 D7 = 6.74   N4 = 1.69979                                                                              ν4 = 55.5                               R8 = 101.55                                                                              D8 =                                                                          Variable                                                           R9 = 117.03                                                                              D9 = 1.00   N5 = 1.88814                                                                              ν5 = 40.8                               R10 = 21.59                                                                              D10 = 4.03                                                         R11 = -90.56                                                                             D11 = 0.80  N6 = 1.80811                                                                              ν6 = 46.6                               R12 = 86.01                                                                              D12 = 4.16                                                         R13 = -19.32                                                                             D13 = 0.80  N7 = 1.77621                                                                              ν7 = 49.6                               R14 = 54.23                                                                              D14 = 4.42  N8 = 1.85501                                                                              ν8 = 23.9                               *R15 = -31.98                                                                            D15 =                                                                         Variable                                                           R16 = -28.47                                                                             D16 = 0.90  N9 = 1.77621                                                                              ν9 = 49.6                               R17 = 47.68                                                                              D17 = 3.35  N10 = 1.81265                                                                             ν10 = 25.4                              R18 = -323.10                                                                            D18 =                                                                         Variable                                                           R19 = (Stop)                                                                             D19 = 1.97                                                         R20 = 143.46                                                                             D20 = 5.63  N11 = 1.72794                                                                             ν11 = 38.0                              R21 = -31.98                                                                             D21 = 0.10                                                         R22 = 84.13                                                                              D22 = 6.57  N12 = 1.50014                                                                             ν12 = 65.0                              R23 = -25.30                                                                             D23 = 1.40  N13 = 1.88814                                                                             ν13 = 40.8                              R24 = -262.85                                                                            D24 = 0.10                                                         R25 = 50.79                                                                              D25 = 7.89  N14 = 1.51356                                                                             ν14 = 51.0                              R26 = -23.63                                                                             D26 = 1.50  N15 = 1.80811                                                                             ν15 = 46.6                              R27 = 89.14                                                                              D27 = 20.14                                                        R28 = 179.23                                                                             D28 = 8.06  N16 = 1.48915                                                                             ν16 = 70.2                              R29 = -34.74                                                                             D29 = 0.15                                                         R30 = -489.23                                                                            D30 = 1.50  N17 = 1.83932                                                                             ν17 = 37.2                              R31 = 35.12                                                                              D31 = 7.02  N18 = 1.48915                                                                             ν18 = 70.2                              R32 = -156.54                                                                            D32 = 0.15                                                         R33 = 201.01                                                                             D33 = 6.82  N19 = 1.51314                                                                             ν19 = 60.5                              R34 = -39.76                                                                             D34 = 1.40  N20 = 1.83932                                                                             ν20 = 37.2                              R35 = -57.60                                                                             D35 = 0.15                                                         R36 = 51.20                                                                              D36 = 5.29  N21 = 1.48915                                                                             ν21 = 70.2                              R37 = -242.74                                                                            D37 = 3.40                                                         R38 = ∞                                                                            D38 = 55.50 N22 = 1.51825                                                                             ν22 = 64.2                              R39 = ∞                                                                 ______________________________________                                        *Aspheric Surface                                                             Variable  Focal Length                                                        Separation                                                                              9.50     15.20  34.20  102.41                                                                              123.50                                 ______________________________________                                        D8        0.80     13.33  28.62  40.37 41.46                                  D15       34.37    19.86  3.07   0.88  3.16                                   D18       10.50    12.48  13.99  4.42  1.06                                   ______________________________________                                        Shape of Asheric Surface                                                      ______________________________________                                        Osculating Sphere: R = -31.983                                                                       Parameter                                              Aspheric Coefficients  Z = 13                                                 A = B = C = 0          F.sub.N0.1 = 1.08                                      D = -5.030 × 10.sup.-11                                                                        F.sub.N0.2 = 0.890                                     E = 3.197 × 10.sup.-13                                                                         β2w = -0.381                                                             hm/ht = 1.10                                           ______________________________________                                        Aspheric Amount                                                                              h          Δ                                             ______________________________________                                        0.7            (6.3 mm)   -0.09 μm                                         0.9            (8.1 mm)   -0.54 μm                                         1.0            (9.0 mm)   -1.05 μm                                         ______________________________________                                        Numerical Example 2                                                           f = 9.5-133.0 Fno = 1:1.7-2.05 2ω = 60.1°-4.74°           ______________________________________                                        R1 = 1703.75                                                                             D1 = 2.50   N1 = 1.81265                                                                              ν1 = 25.4                               R2 = 106.53                                                                              D2 = 6.44                                                          R3 = 763.82                                                                              D3 = 8.23   N2 = 1.43496                                                                              ν2 = 95.1                               R4 = -122.79                                                                             D4 = 0.15                                                          R5 = 92.73 D5 = 13.31  N3 = 1.49845                                                                              ν3 = 81.6                               R6 = -146.48                                                                             D6 = 0.15                                                          R7 = 48.60 D7 = 7.20   N4 = 1.69979                                                                              ν4 = 55.5                               R8 = 91.04 D8 =                                                                          Variable                                                           R9 = 115.10                                                                              D9 = 1.00   N5 = 1.88814                                                                              ν5 = 40.8                               R10 = 18.70                                                                              D10 = 3.64                                                         R11 = -56.81                                                                             D11 = 0.80  N6 = 1.80811                                                                              ν6 = 46.6                               R12 = 98.00                                                                              D12 = 4.04                                                         *R13 = -14.32                                                                            D13 = 0.80  N7 = 1.77621                                                                              ν7 = 49.6                               R14 = 138.11                                                                             D14 = 4.74  N8 = 1.85501                                                                              ν8 = 23.9                               R15 = -23.37                                                                             D15 =                                                                         Variable                                                           R16 = -31.46                                                                             D16 = 0.90  N9 = 1.77621                                                                              ν9 = 49.6                               R17 = 40.12                                                                              D17 = 4.27  N10 = 1.85501                                                                             ν10 = 23.9                              R18 = 1585.12                                                                            D18 =                                                                         Variable                                                           R19 = (Stop)                                                                             D19 = 1.81                                                         R20 = -518.14                                                                            D20 = 5.19  N11 = 1.72794                                                                             ν11 = 38.0                              R21 = -36.89                                                                             D21 = 0.10                                                         R22 = 94.66                                                                              D22 = 7.82  N12 = 1.50014                                                                             ν12 = 65.0                              R23 = -30.42                                                                             D23 = 1.40  N13 = 1.88814                                                                             ν13 = 40.8                              R24 = -101.62                                                                            D24 = 0.10                                                         R25 = 39.37                                                                              D25 = 10.42 N14 = 1.51356                                                                             ν14 = 51.0                              R26 = -33.16                                                                             D26 = 1.50  N15 = 1.80811                                                                             ν15 = 46.6                              R27 = 277.25                                                                             D27 = 13.95                                                        R28 = 1015.97                                                                            D28 = 7.37  N16 = 1.48915                                                                             ν16 = 70.2                              R29 = -41.90                                                                             D29 = 0.15                                                         R30 = 68.12                                                                              D30 = 1.50  N17 = 1.83932                                                                             ν17 = 37.2                              R31 = 24.32                                                                              D31 = 8.68  N18 = 1.48915                                                                             ν18 = 70.2                              R32 = -1018.30                                                                           D32 = 0.15                                                         R33 = 101.48                                                                             D33 = 6.81  N19 = 1.51314                                                                             ν19 = 60.5                              R34 = -39.46                                                                             D34 = 1.40  N20 = 1.83932                                                                             ν20 = 37.2                              R35 = -1105.61                                                                           D35 = 0.15                                                         R36 = 56.41                                                                              D36 = 6.45  N21 = 1.48915                                                                             ν21 = 70.2                              R37 = -66.16                                                                             D37 = 3.40                                                         R38 = ∞                                                                            D38 = 55.50 N22 = 1.51825                                                                             ν22 = 64.2                              R39 = ∞                                                                 ______________________________________                                        *Aspheric Surface                                                             Variable  Focal Length                                                        Separation                                                                              9.50     15.20  35.15  110.58                                                                              133.00                                 ______________________________________                                        D8        1.97     16.12  33.51  46.77 48.05                                  D15       47.43    31.07  10.57  1.00  1.85                                   D18       1.50     3.71   6.81   3.13  0.99                                   ______________________________________                                        Shape of Asheric Surface                                                      ______________________________________                                        Osculating Sphere: R = -14.328                                                                       Parameter                                              Aspheric Coefficients  Z = 14                                                 A = B = C = 0          F.sub.N0.1 = 1.06                                      D = 9.659 × 10.sup.-10                                                                         F.sub.N0.2 = 0.679                                     E = -6.497 × 10.sup.-12                                                                        β2w = -0.273                                                             hm/ht = 1.09                                           ______________________________________                                        Aspheric Amount                                                                              h          Δ                                             ______________________________________                                        0.7            (5.67 mm)  0.81 μm                                          0.9            (7.29 mm)  4.95 μm                                          1.0            (8.10 mm)  10.00 μm                                         ______________________________________                                        Numerical Example 3                                                           f = 10.0-250 Fno = 1:1.8-2.5 2ω = 57.6°-2.52°             ______________________________________                                        R1 = 242.57                                                                              D1 = 2.50   N1 = 1.81265                                                                              ν1 = 25.4                               R2 = 126.54                                                                              D2 = 10.14                                                         R3 = 852.19                                                                              D3 = 7.62   N2 = 1.43496                                                                              ν2 = 95.1                               R4 = -341.40                                                                             D4 = 0.15                                                          R5 = 119.29                                                                              D5 = 17.31  N3 = 1.49845                                                                              ν3 = 81.6                               R6 = -346.13                                                                             D6 = 0.15                                                          R7 = 82.75 D7 = 4.95   N4 = 1.69979                                                                              ν4 = 55.5                               R8 = 98.90 D8 =                                                                          Variable                                                           R9 = 51.58 D9 = 1.00   N5 = 1.88814                                                                              ν5 = 40.8                               R10 = 20.17                                                                              D10 = 5.39                                                         R11 = -904.89                                                                            D11 = 0.80  N6 = 1.80811                                                                              ν6 = 46.6                               *R12 = -1554.33                                                                          D12 = 3.86                                                         R13 = -24.45                                                                             D13 = 0.80  N7 = 1.77621                                                                              ν7 = 49.6                               R14 = 22.22                                                                              D14 = 7.26  N8 = 1.85501                                                                              ν8 = 23.9                               R15 = -90.83                                                                             D15 =                                                                         Variable                                                           R16 = -43.28                                                                             D16 = 0.90  N9 = 1.77621                                                                              ν9 = 49.6                               R17 = 48.32                                                                              D17 = 6.97  N10 = 1.81265                                                                             ν10 = 25.4                              R18 = -468.63                                                                            D18 =                                                                         Variable                                                           R19 = (Stop)                                                                             D19 = 1.79                                                         R20 = -348.81                                                                            D20 = 5.71  N11 = 1.72794                                                                             ν11 = 38.0                              R21 = -63.07                                                                             D21 = 0.10                                                         R22 = 48.36                                                                              D22 = 15.58 N12 = 1.50014                                                                             ν12 = 65.0                              R23 = -45.84                                                                             D23 = 1.40  N13 = 1.88814                                                                             ν13 = 40.8                              R24 = -112.26                                                                            D24 = 0.10                                                         R25 = 105.29                                                                             D25 = 3.16  N14 = 1.48915                                                                             ν14 = 70.2                              R26 = 107.59                                                                             D26 = 12.47                                                        R27 = 48.21                                                                              D27 = 11.35 N15 = 1.48915                                                                             ν15 = 70.2                              R28 = -85.93                                                                             D28 = 0.15                                                         R29 = -157.51                                                                            D29 = 1.50  N16 = 1.83932                                                                             ν16 = 37.2                              R30 = 30.02                                                                              D30 = 11.53 N17 = 1.48915                                                                             ν17 = 70.2                              R31 = -70.68                                                                             D31 = 0.15                                                         R32 = 41.98                                                                              D32 = 9.93  N18 = 1.51314                                                                             ν18 = 60.5                              R33 = -41.00                                                                             D33 = 1.40  N19 = 1.83932                                                                             ν19 = 37.2                              R34 = 121.61                                                                             D34 = 0.15                                                         R35 = 43.59                                                                              D35 = 4.91  N20 = 1.48915                                                                             ν20 = 70.2                              R36 = 92.49                                                                              D36 = 3.40                                                         R37 = ∞                                                                            D37 = 55.50 N21 = 1.51825                                                                             ν21 = 64.2                              R38 = ∞                                                                 ______________________________________                                        *Aspheric Surface                                                             Variable  Focal Length                                                        Separation                                                                              10.00    16.00  31.62  170.00                                                                              250.00                                 ______________________________________                                        D8        0.86     34.56  70.11  116.59                                                                              122.19                                 D15       132.55   95.54  54.85  3.20  2.36                                   D18       2.00     5.31   10.45  15.62 10.85                                  ______________________________________                                        Shape of Asheric Surface                                                      ______________________________________                                        Osculating Sphere: R = -1554.334                                                                     Parameter                                              Aspheric Coefficients  Z = 25                                                 A = B = E = 0          F.sub.N0.1 = 1.60                                      C = -2.723 × 10.sup.-8                                                                         F.sub.N0.2 = 0.868                                     D = 1.812 × 10.sup.-10                                                                         β2w  = -0.163                                                            hm/ht = 1.19                                           ______________________________________                                        Aspheric Amount                                                                              h          Δ                                             ______________________________________                                        0.7            (7.21 mm)  -2.50 μm                                         0.9            (9.27 mm)  -7.39 μm                                         1.0            (10.30 mm) -9.55 μm                                         ______________________________________                                        Numerical Example 4                                                           f = 10.0-250 Fno = 1:1.8-2.5 2ω = 57.6°-2.52°             ______________________________________                                        R1 = 2410.58                                                                             D1 = 2.50   N1 = 1.81265                                                                              ν1 = 25.4                               R2 = 237.10                                                                              D2 = 8.99                                                          R3 = -4779.95                                                                            D3 = 10.96  N2 = 1.43496                                                                              ν2 = 95.1                               R4 = -197.31                                                                             D4 = 0.15                                                          R5 = 160.90                                                                              D5 = 14.57  N3 = 1.49845                                                                              ν3 = 81.6                               R6 = -564.41                                                                             D6 = 0.15                                                          R7 = 108.51                                                                              D7 = 7.14   N4 = 1.69979                                                                              ν4 = 55.5                               R8 = 187.46                                                                              D8 =                                                                          Variable                                                           R9 = 64.67 D9 = 1.00   N5 = 1.88814                                                                              ν5 = 40.8                               R10 = 28.76                                                                              D10 = 7.40                                                         R11 = -150.75                                                                            D11 = 0.80  N6 = 1.80811                                                                              ν6 = 46.6                               R12 = -293.88                                                                            D12 = 4.55                                                         R13 = -36.26                                                                             D13 = 0.80  N7 = 1.77621                                                                              ν7 = 49.6                               R14 = 34.15                                                                              D14 = 6.98  N8 = 1.85501                                                                              ν8 = 23.9                               *R15 = -163.75                                                                           D15 =                                                                         Variable                                                           R16 = -45.10                                                                             D16 = 0.90  N9 = 1.77621                                                                              ν9 = 49.6                               R17 = 34.51                                                                              D17 = 4.75  N10 = 1.81265                                                                             ν10 = 25.4                              R18 = 1631.97                                                                            D18 =                                                                         Variable                                                           R19 = (Stop)                                                                             D19 = 1.94                                                         R20 = -255.80                                                                            D20 = 4.17  N11 = 1.72794                                                                             ν11 = 38.0                              R21 = -60.57                                                                             D21 = 0.10                                                         R22 = 82.07                                                                              D22 = 8.89  N12 = 1.48915                                                                             ν12 = 70.2                              R23 = -33.60                                                                             D23 = 1.40  N13 = 1.83932                                                                             ν13 = 37.2                              R24 = -153.09                                                                            D24 = 0.10                                                         R25 = 59.05                                                                              D25 = 5.89  N14 = 1.48915                                                                             ν14 = 70.2                              R26 = 5032.81                                                                            D26 = 19.17                                                        R27 = 709.25                                                                             D27 = 5.24  N15 = 1.48915                                                                             ν15 = 70.2                              R28 = -76.03                                                                             D28 = 0.15                                                         R29 = -1979.45                                                                           D29 = 1.50  N16 = 1.83932                                                                             ν16 = 37.2                              R30 = 39.25                                                                              D30 = 8.26  N17 = 1.48915                                                                             ν17 = 70.2                              R31 = -71.46                                                                             D31 = 0.15                                                         R32 = 72.55                                                                              D32 = 7.78  N18 = 1.51314                                                                             ν18 = 60.5                              R33 = -44.13                                                                             D33 = 1.40  N19 = 1.83932                                                                             ν19 = 37.2                              R34 = -108.98                                                                            D34 = 0.15                                                         R35 = 56.56                                                                              D35 = 4.00  N20 = 1.48915                                                                             ν20 = 70.2                              R36 = 89.10                                                                              D36 = 3.40                                                         R37 = ∞                                                                            D37 = 55.50 N21 = 1.51825                                                                             ν21 = 64.2                              R38 = ∞                                                                 ______________________________________                                        *Aspheric Surface                                                             Variable  Focal Length                                                        Separation                                                                              10.00    16.00  31.62  170.00                                                                              250.00                                 ______________________________________                                        D8        2.48     35.02  69.69  116.37                                                                              121.55                                 D15       117.72   82.39  43.74  1.73  5.07                                   D18       8.00     10.79  14.77  10.10 1.58                                   ______________________________________                                        Shape of Asheric Surface                                                      ______________________________________                                        Osculating Sphere: R = -163.750                                                                      Parameter                                              Aspheric Coefficients  Z = 25                                                 A = B = C = 0          F.sub.N0.1 = 1.60                                      D = -5.784 × 10.sup.-12                                                                        F.sub.N0.2 = 1.21                                      E = 1.859 × 10.sup.-14                                                                         β2w = -0.230                                                             hm/ht = 1.24                                           ______________________________________                                        Aspheric Amount                                                                              h          Δ                                             ______________________________________                                        0.7             (8.12 mm) -0.08 μm                                         0.9            (10.44 mm) -0.53 μm                                         1.0            (11.60 mm) -1.08 μm                                         ______________________________________                                        Numerical Example 5                                                           f = 9.5-104.5 Fno = 1:1.7 2ω = 60.1°-6.03°                ______________________________________                                        R1 = 909.50                                                                              D1 = 2.50   N1 = 1.81265                                                                              ν1 = 25.4                               R2 = 100.71                                                                              D2 = 4.08                                                          R3 = 195.83                                                                              D3 = 9.04   N2 = 1.43496                                                                              ν2 = 95.1                               R4 = -155.81                                                                             D4 = 0.15                                                          R5 = 79.12 D5 = 11.26  N3 = 1.49845                                                                              ν3 = 81.6                               R6 = -212.24                                                                             D6 = 0.15                                                          R7 = 51.91 D7 = 7.11   N4 = 1.69979                                                                              ν4 = 55.5                               R8 = 118.00                                                                              D8 =                                                                          Variable                                                           R9 = 96.71 D9 = 1.00   N5 = 1.88814                                                                              ν5 = 40.8                               R10 = 22.19                                                                              D10 = 3.86                                                         R11 = -126.84                                                                            D11 = 0.80  N6 = 1.80811                                                                              ν6 = 46.6                               R12 = 59.53                                                                              D12 = 4.48                                                         R13 = -19.14                                                                             D13 = 0.80  N7 = 1.77621                                                                              ν7 = 49.6                               R14 = 69.53                                                                              D14 = 4.23  N8 = 1.85501                                                                              ν8 = 23.9                               *R15 = -31.96                                                                            D15 =                                                                         Variable                                                           R16 = -30.49                                                                             D16 = 0.90  N9 = 1.77621                                                                              ν9 = 49.6                               R17 = 40.95                                                                              D17 = 3.54  N10 = 1.81265                                                                             ν10 = 25.4                              R18 = -665.19                                                                            D18 =                                                                         Variable                                                           R19 = (Stop)                                                                             D19 = 1.99                                                         R20 = 178.66                                                                             D20 = 5.35  N11 = 1.72794                                                                             ν11 = 38.0                              R21 = -31.00                                                                             D21 = 0.10                                                         R22 = 69.61                                                                              D22 = 6.43  N12 = 1.50014                                                                             ν12 = 65.0                              R23 = -25.03                                                                             D23 = 1.40  N13 = 1.88814                                                                             ν13 = 40.8                              R24 = -358.92                                                                            D24 = 0.10                                                         R25 = 50.13                                                                              D25 = 7.40  N14 = 1.51356                                                                             ν14 = 51.0                              R26 = -24.35                                                                             D26 = 1.50  N15 = 1.80811                                                                             ν15 = 46.6                              R27 = 80.52                                                                              D27 = 20.29                                                        R28 = 195.02                                                                             D28 = 7.98  N16 = 1.48915                                                                             ν16 = 70.2                              R29 = -34.86                                                                             D29 = 0.15                                                         R30 = -11249.89                                                                          D30 = 1.50  N17 = 1.83932                                                                             ν17 = 37.2                              R31 = 36.13                                                                              D31 = 6.95  N18 = 2.48915                                                                             ν18 = 70.2                              R32 = -140.23                                                                            D32 = 0.15                                                         R33 = 307.31                                                                             D33 = 6.18  N19 = 1.51314                                                                             ν19 = 60.5                              R34 = -39.20                                                                             D34 = 1.40  N20 = 1.83932                                                                             ν20 = 37.2                              R35 = -61.91                                                                             D35 = 0.15                                                         R36 = 50.12                                                                              D36 = 5.76  N21 = 1.48915                                                                             ν21 = 70.2                              R37 = -162.77                                                                            D37 = 3.40                                                         R38 = ∞                                                                            D38 = 55.50 N22 = 1.51825                                                                             ν22 = 64.2                              R39 = ∞                                                                 ______________________________________                                        *Aspheric Surface                                                             Variable  Focal Length                                                        Separation                                                                              9.50     15.20  30.04  57.95 104.50                                 ______________________________________                                        D8        0.65     13.27  26.56  35.31 40.29                                  D15       36.57    21.99  7.17   0.82  3.20                                   D18       7.50     9.47   10.99  8.60  1.24                                   ______________________________________                                        Shape of Asheric Surface                                                      ______________________________________                                        Osculating Sphere: R = -31.968                                                                       Parameter                                              Aspheric Coefficients  Z = 11                                                 A = B = C = 0          F.sub.N0.R = 1.0                                       D = 3.246 × 10.sup.-11                                                                         F.sub.N0.1 = 1.06                                      E = -1.102 × 10.sup.-13                                                                        F.sub.N0.2 = 0.882                                                            β2w = -0.381                                                             ht/hz = 1.24                                           ______________________________________                                        Aspheric Amount                                                                              h          Δ                                             ______________________________________                                        0.7            (6.35 mm)  -0.07 μm                                         0.9            (8.16 mm)  -0.49 μm                                         1.0            (9.07 mm)  -1.07 μm                                         ______________________________________                                        Numerical Example 6                                                           f = 10.0-110.0 Fno = 1:1.7 2ω = 57.6°-5.72°               ______________________________________                                        R1 = 924.81                                                                              D1 = 2.50   N1 = 1.81265                                                                              ν1 = 25.4                               R2 = 95.22 D2 = 6.84                                                          R3 = 4394.05                                                                             D3 = 7.12   N2 = 1.43496                                                                              ν2 = 95.1                               R4 = -120.99                                                                             D4 = 0.15                                                          R5 = 84.76 D5 = 14.01  N3 = 1.49845                                                                              ν3 = 81.6                               R6 = -139.82                                                                             D6 = 0.15                                                          R7 = 51.07 D7 = 7.78   N4 = 1.69979                                                                              ν4 = 55.5                               R8 = 105.33                                                                              D8 =                                                                          Variable                                                           R9 = 91.51 D9 = 1.00   N5 = 1.88814                                                                              ν5 = 40.8                               R10 = 18.15                                                                              D10 = 3.48                                                         R11 = -84.71                                                                             D11 = 0.80  N6 = 1.80811                                                                              ν6 = 46.6                               R12 = 163.60                                                                             D12 = 3.21                                                         *R13 = -17.68                                                                            D13 = 0.80  N7 = 1.77621                                                                              ν7 = 49.6                               R14 = 33.42                                                                              D14 = 5.17  N8 = 1.85501                                                                              ν8 = 23.9                               R15 = -38.40                                                                             D15 =                                                                         Variable                                                           R16 = -30.83                                                                             D16 = 0.90  N9 = 1.77621                                                                              ν9 = 49.6                               R17 = 50.41                                                                              D17 = 3.99  N10 = 1.85501                                                                             ν10 = 23.9                              R18 = -664.04                                                                            D18 =                                                                         Variable                                                           R19 = (Stop)                                                                             D19 = 1.79                                                         R20 = -696.10                                                                            D20 = 5.33  N11 = 1.72794                                                                             ν11 = 38.0                              R21 = -38.24                                                                             D21 = 0.10                                                         R22 = 92.97                                                                              D22 = 8.04  N12 = 1.50014                                                                             ν12 = 65.0                              R23 = -31.74                                                                             D23 = 1.40  N13 = 1.88814                                                                             ν13 = 40.8                              R24 = -93.14                                                                             D24 = 0.10                                                         R25 = 40.20                                                                              D25 = 11.25 N14 = 1.51356                                                                             ν14 = 51.0                              R26 = -33.88                                                                             D26 = 1.50  N15 = 1.80811                                                                             ν15 = 46.6                              R27 = 177.49                                                                             D27 = 13.31                                                        R28 = 390.80                                                                             D28 = 7.79  N16 = 1.48915                                                                             ν16 = 70.2                              R29 = -41.40                                                                             D29 = 0.15                                                         R30 = 75.89                                                                              D30 = 1.50  N17 = 1.83932                                                                             ν17 = 37.2                              R31 = 24.77                                                                              D31 = 8.90  N18 = 1.48915                                                                             ν18 = 70.2                              R32 = -555.75                                                                            D32 = 0.15                                                         R33 = 158.45                                                                             D33 = 6.98  N19 = 1.51314                                                                             ν19 = 60.5                              R34 = -40.43                                                                             D34 = 1.40  N20 = 1.83932                                                                             ν20 = 37.2                              R35 = -308.63                                                                            D35 = 0.15                                                         R36 = 51.08                                                                              D36 = 6.78  N21 = 1.48915                                                                             ν21 = 70.2                              R37 = -86.52                                                                             D37 = 3.40                                                         R38 = ∞                                                                            D38 = 55.50 N22 = 1.51825                                                                             ν22 = 64.2                              R39 = ∞                                                                 ______________________________________                                        *Aspheric Surface                                                             Variable  Focal Length                                                        Separation                                                                              10.00    16.00  33.00  61.00 110.00                                 ______________________________________                                        D8        0.88     14.97  30.40  39.26 45.08                                  D15       48.74    32.27  13.86  4.67  2.66                                   D18       1.50     3.88   6.86   7.19  3.38                                   ______________________________________                                        Shape of Asheric Surface                                                      ______________________________________                                        Osculating Sphere: R = -17.680                                                                       Parameter                                              Aspheric Coefficients  Z = 11                                                 A = B = C = 0          F.sub.N0.R = 1.0                                       D = -4.468 × 10.sup.-10                                                                        F.sub.N0.1 = 1.05                                      E = 1.526 × 10.sup.-12                                                                         F.sub.N0.2 = 0.680                                                            β2w = -0.279                                                             ht/hz = 1.24                                           ______________________________________                                        Aspheric Amount                                                                              h          Δ                                             ______________________________________                                        0.7            (5.95 mm)  -0.62 μm                                         0.9            (7.65 mm)  -4.19 μm                                         1.0            (8.50 mm)  -9.17 μm                                         ______________________________________                                        Numerical Example 7                                                           f = 10.0-170.0 Fno = 1:1.8 2ω = 57.6°-3.71°               ______________________________________                                        R1 = 484.44                                                                              D1 = 2.50   N1 = 1.81265                                                                              ν1 = 25.4                               R2 = 147.75                                                                              D2 = 14.45                                                         R3 = -284.94                                                                             D3 = 5.49   N2 = 1.43496                                                                              ν2 = 95.1                               R4 = -174.10                                                                             D4 = 0.15                                                          R5 = 143.58                                                                              D5 = 15.68  N3 = 1.49845                                                                              ν3 = 81.6                               R6 = -272.35                                                                             D6 = 0.15                                                          R7 = 107.99                                                                              D7 = 7.87   N4 = 1.69979                                                                              ν4 = 55.5                               R8 = 225.28                                                                              D8 =                                                                          Variable                                                           R9 = 46.50 D9 = 1.00   N5 = 1.88814                                                                              ν5 = 40.8                               R10 = 21.80                                                                              D10 = 5.52                                                         R11 = -206.83                                                                            D11 = 0.80  N6 = 1.80811                                                                              ν6 = 46.6                               *R12 = 1041.43                                                                           D12 = 4.27                                                         R13 = -26.41                                                                             D13 = 0.80  N7 = 1.77621                                                                              ν7 = 49.6                               R14 = 23.95                                                                              D14 = 6.33  N8 = 1.85501                                                                              ν8 = 23.9                               R15 = -115.31                                                                            D15 =                                                                         Variable                                                           R16 = -46.57                                                                             D16 = 0.90  N9 = 1.77621                                                                              ν9 = 49.6                               R17 = 47.89                                                                              D17 = 6.60  N10 = 1.81265                                                                             ν10 = 25.4                              R18 = -889.82                                                                            D18 =                                                                         Variable                                                           R19 = (Stop)                                                                             D19 = 1.80                                                         R20 = -456.22                                                                            D20 = 5.84  N11 = 1.72794                                                                             ν11 = 38.0                              R21 = -59.95                                                                             D21 = 0.10                                                         R22 = 49.94                                                                              D22 = 13.82 N12 = 1.50014                                                                             ν12 = 65.0                              R23 = -47.13                                                                             D23 = 1.40  N13 = 1.88814                                                                             ν13 = 40.8                              R24 = -165.82                                                                            D24 = 0.10                                                         R25 = 104.16                                                                             D25 = 3.19  N14 = 1.48915                                                                             ν14 = 70.2                              R26 = 107.98                                                                             D26 = 20.10                                                        R27 = 46.24                                                                              D27 = 11.11 N15 = 1.48915                                                                             ν15 = 70.2                              R28 = -99.66                                                                             D28 = 0.15                                                         R29 = -492.26                                                                            D29 = 0.15  N16 = 1.83932                                                                             ν16 = 37.2                              R30 = 30.11                                                                              D30 = 11.26 N17 = 1.48915                                                                             ν17 = 70.2                              R31 = -75.31                                                                             D31 = 0.15                                                         R32 = 45.44                                                                              D32 = 9.53  N18 = 1.51314                                                                             ν18 = 60.5                              R33 = -41.24                                                                             D33 = 1.40  N19 = 1.83932                                                                             ν19 = 37.2                              R34 = 108.59                                                                             D34 = 0.15                                                         R35 = 47.95                                                                              D35 = 5.03  N20 = 1.48915                                                                             ν20 = 70.2                              R36 = 163.61                                                                             D36 = 3.40                                                         R37 = ∞                                                                            D37 = 55.50 N21 = 1.51825                                                                             ν21 = 64.2                              R38 = ∞                                                                 ______________________________________                                        *Aspheric Surface                                                             Variable  Focal Length                                                        Separation                                                                              10.00    16.00  40.00  90.00 170.00                                 ______________________________________                                        D8        3.05     35.62  78.99  102.48                                                                              114.78                                 D15       127.65   91.55  40.90  12.83 2.50                                   D18       1.50     5.03   12.31  16.90 14.92                                  ______________________________________                                        Shape of Asheric Surface                                                      ______________________________________                                        Osculating Sphere: R = 1041.431                                                                      Parameter                                              Aspheric Coefficients  Z = 17                                                 A = B = C = 0          F.sub.N0.R = 1.0                                       D = 1.358 × 10.sup.-10                                                                         F.sub.N0.1 = 1.59                                      E = -5.379 × 10.sup.-13                                                                        F.sub.N0.2 = 0.906                                                            β2w = -0.169                                                             ht/hz = 1.26                                           ______________________________________                                        Aspheric Amount                                                                              h          Δ                                             ______________________________________                                        0.7            (7.14 mm)  0.73 μm                                          0.9            (9.18 mm)  4.56 μm                                          1.0            (10.20 mm) 9.35 μm                                          ______________________________________                                        Numerical Example 8                                                           f = 10.0-170.0 Fno = 1:1.8 2ω = 57.6°-3.71°               ______________________________________                                        R1 = 878.09                                                                              D1 = 2.50   N1 = 1.81265                                                                              ν1 = 25.4                               R2 = 197.50                                                                              D2 = 7.33                                                          R3 = 1079.40                                                                             D3 = 9.55   N2 = 1.43496                                                                              ν2 = 95.1                               R4 = -259.01                                                                             D4 = 0.15                                                          R5 = 152.27                                                                              D5 = 14.44  N3 = 1.49845                                                                              ν3 = 81.6                               R6 = -374.62                                                                             D6 = 0.15                                                          R7 = 106.12                                                                              D7 = 6.47   N4 = 1.69979                                                                              ν4 = 55.5                               R8 = 181.12                                                                              D8 =                                                                          Variable                                                           R9 = 62.40 D9 = 1.00   N5 = 1.88814                                                                              ν5 = 40.8                               R10 = 28.87                                                                              D10 = 6.99                                                         R11 = -133.04                                                                            D11 = 0.80  N6 = 1.80811                                                                              ν6 = 46.6                               R12 = -362.12                                                                            D12 = 4.31                                                         R13 = -35.76                                                                             D13 = 0.80  N7 = 1.77621                                                                              ν7 = 49.6                               R14 = 32.31                                                                              D14 = 6.57  N8 = 1.85501                                                                              ν8 = 23.9                               *R15 = -198.20                                                                           D15 =                                                                         Variable                                                           R16 = -45.72                                                                             D16 = 0.90  N9 = 1.77621                                                                              ν9 = 49.6                               R17 = 34.09                                                                              D17 = 4.66  N10 = 1.81265                                                                             ν10 = 25.4                              R18 = 1107.18                                                                            D18 =                                                                         Variable                                                           R19 = (Stop)                                                                             D19 = 3.00                                                         R20 = -24.510                                                                            D20 = 3. 82 N11 = 1.72794                                                                             ν11 = 38.0                              R21 = -58.56                                                                             D21 = 0.10                                                         R22 = 72.48                                                                              D22 = 8.08  N12 = 1.48915                                                                             ν12 = 70.2                              R23 = -30.74                                                                             D23 = 1.40  N13 = 1.83932                                                                             ν13 = 37.2                              R24 = -169.98                                                                            D24 = 0.10                                                         R25 = 57.84                                                                              D25 = 5.33  N14 = 1.48915                                                                             ν14 = 70.2                              R26 = 3334.59                                                                            D26 = 19.36                                                        R27 = 3092.49                                                                            D27 = 4.84  N15 = 1.48915                                                                             ν15 = 70.2                              R28 = -75.38                                                                             D28 = 0.15                                                         R29 = -1677.98                                                                           D29 = 1.15  N16 = 1.83932                                                                             ν16 = 37.2                              R30 = 38.96                                                                              D30 = 7.85  N17 = 1.48915                                                                             ν17 = 70.2                              R31 = -69.60                                                                             D31 = 0.15                                                         R32 = 91.81                                                                              D32 = 6.86  N18 = 1.51314                                                                             ν18 = 60.5                              R33 = -49.43                                                                             D33 = 1.40  N19 = 1.83932                                                                             ν19 = 37.2                              R34 = -96.69                                                                             D34 = 0.15                                                         R35 = 46.60                                                                              D35 = 4.59  N20 = 1.48915                                                                             ν20 = 70.2                              R36 = 119.00                                                                             D36 = 3.40                                                         R37 = ∞                                                                            D37 = 55.50 N21 = 1.51825                                                                             ν21 = 64.2                              R38 = ∞                                                                 ______________________________________                                        *Aspheric Surface                                                             Variable  Focal Length                                                        Separation                                                                              10.00    16.00  40.00  90.00  170.00                                ______________________________________                                        D8        1.06     31.49  72.53  95.40  107.29                                D15       109.81   76.48  30.19  6.68   2.08                                  D18       1.50     4.39   9.64   10.28  3.00                                  ______________________________________                                        Shape of Asheric Surface                                                      ______________________________________                                        Osculating Sphere: R = -198.207                                                                      Parameter                                              Aspheric Coefficients  Z = 17                                                 A = B = C = 0          F.sub.N0.R = 1.0                                       D = 1.034 × 10.sup.-11                                                                         F.sub.N0.1 = 1.59                                      E = -3.980 × 10.sup.-14                                                                        F.sub.N0.2 = 1.22                                                             β2w = -0.215                                                             ht/hz = 1.226                                          ______________________________________                                        Aspheric Amount                                                                              h          Δ                                             ______________________________________                                        0.7            (7.59 mm)  0.09 μm                                          0.9            (9.76 mm)  0.54 μm                                          1.0            (10.84 mm) 1.08 μm                                          ______________________________________                                    

According to the invention, as has been described above, in applicationto the so-called 4-unit zoom lens, the lateral magnification for thewide-angle end of the lens unit for varying the focal length and theF-number of each of the certain lens units are properly determined andthe aspheric sphere is applied to at least one of lens surfaces whichsatisfies the prescribed condition for the height of incidence of theaxial light beam. When the zoom lens embodies these features, the rangeof variation of spherical aberration with zooming is greatly reduced.Further, astigmatism, curvature of field, distortion and other off-axialaberrations are corrected in good balance over the entire zooming range.Thus, it is made possible to achieve a large relative aperture, highrange zoom lens whose F-number for the wide-angle end is 1.7 orthereabout and whose zoom ratio is 10 to 25, while still maintaininggood stability of high optical performance throughout the entire zoomingrange.

The foregoing embodiment has been described in connection with theprovision of the aspheric surface in the second lens unit, as emphasisis laid on correction of spherical aberration. In the following, anotherembodiment is described where an aspheric surface is introduced into thethird lens unit with a chief aim at correcting on-axial aberrations.

FIG. 22, FIG. 23 and FIG. 24 in lens block diagram show numericalexamples 9, 10 and 11 of zoom lenses of the invention in the wide-angleend.

In FIG. 22 and FIG. 23, F denotes a first or focusing lens unit (frontlens unit) of positive refractive power which is divided into a frontpart F1 of negative refractive power and a rear part F2 of positiverefractive power. As the object distance varies, focusing is carried outby moving the front focusing unit F1 along an optical axis.

In the example 11 of FIG. 24, the focusing lens unit F is constructed inthe unified form so that it is entirely moved axially for focusing.

V denotes a second lens unit for varying the focal length, or variatorof negative refractive power. It moves axially toward the image sidemonotonously to vary the focal length from the wide-angle end to thetelephoto end. C denotes a compensator of positive refractive power. Tocompensate for the image shift with zooming, the compensator C movesaxially toward the object side non-linearly. The variator V and thecompensator C are used where the magnification takes -1x (unitymagnification) at a time during zooming. SP (R31) stands for a stop. Rdenotes a relay lens unit of positive refractive power. G denotes acolor separation prism or an optical filter shown as a glass block inFIGS. 22 to 24.

The features of the zoom lens which are characteristic of the presentembodiment are described below.

To realize a zoom lens having a zoom ratio Z of 10 or greater andfurther whose aperture ratio is much increased over the entire zoomingrange, the first feature of the invention is to make use of what is sofast as to satisfy the before-described condition (3) in the front lensunit F. Particularly for the telephoto end, the value F_(NO).t of theF-number is so much fast. Another feature is to employ such a zoomingarrangement that the variator V and the compensator C each move past apoint for -1x magnification and are given an individual high rate ofvariable power.

In particular, the variator V takes a rate of variable power thatsatisfies the before-described conditions (4) and (5). This assures agreat increase of the zoom ratio. Moreover, the effective F-number ofthe compensator C, too, is maintained at so fast a value F_(NO).3 as tosatisfy the before-described condition (6), thus making it easier toincrease the aperture ratio. With these in effect, of all theaberrations which vary with zooming, the spherical aberration whichwould otherwise vary to large extent particularly when zooming goesthrough the neighborhood of the start point fM of F drop, is wellsuppressed as shown in FIG. 29.

The height of incidence of the ray of maximum diameter of an axial lightbeam on the lens units increases to the highest at a time when the Fdrop starts (in the zooming position fM) as shown in FIGS. 30(A) to30(C), or where spherical aberration is most over-corrected. In theother region of the zooming range, it is lower than that. It is to benoted that FIGS. 30(A) to 30(C) show the optical paths in a partialoptical system of the zoom lens of FIG. 22 in different zoomingpositions.

In the present embodiment, to utilize this optical property, thecompensator C, to which the above-stated condition is applied, isprovided with a lens surface for correcting spherical aberration. Forthis purpose, at least one cemented lens is put within the interior ofthe compensator C and its cemented surface is made to be a divergentsurface for spherical aberration. For such a cemented surface toincrease the effect of diverging spherical aberration, the media on thefront and rear sides of that boundary surface are made to differ inrefractive index from each other by an amount Δn as defined in thefollowing condition (7):

    0.17<Δn . . .                                        (7)

When this condition is satisfied, variation with zooming of sphericalaberrations in lower terms is corrected well.

According to the invention, the compensator C has its effective F-numberF_(NO).3 become very fast. The zoom lens is, therefore, over-correctedfor spherical aberrations of higher order. This lays limitation onincreasing of the aperture ratio, in the design of using only sphericallenses.

So, in the present embodiment, the compensator C is made up by using atleast one aspheric surface. At a time when the F drop starts, the heightof incidence of the axial light beam appears highest at a value h3m and,when zoomed to the telephoto end, because of the F drop, lowers to avalue h3T. Their ratio lies within the range given by the followingcondition (8):

    1.15<h3m/h3T . . .                                         (8)

Thus, the residual spherical aberrations of higher order are canceled.

Particularly for the spherical aberrations of higher order to correctwell, the aspheric surface is formed to such a shape that the centralzone of the aspheric surface is almost spherical, and the nearer to themargin, the more aspherical.

It should be explained that the condition described above lets theaspheric surface take full effect on the zooming system of the zoom lensonly in that very narrow region of the zooming range which lies aroundthe start point of the F drop and give as little adverse influence tospherical aberration and astigmatism as possible in the other regions ofthe zooming range.

When the ratio of h3m to h3T in the condition (8) is nearer to 1 thanthe limit, as this means that the height of incidence of the axial lightbeam on the aspheric surface changes little during zooming from theneighborhood of the F drop to the telephoto end, the aspheric surfaceexerts the effect of correcting spherical aberration not only around thestart point of the F drop, but also extends its influence up to thetelephoto end in respect to spherical aberration.

If the spherical aberration in the zooming position fM (=(F_(NO).w/F_(NO).t) x ft) is corrected by the aspheric surface in the underdirection, the spherical aberration in the telephoto end, too, would, onreceipt of the influence of this aspheric surface, change in the underdirection. Hence, the effect of correcting the variation of sphericalaberration is objectionably weakened.

It will be appreciated from the above description that in the presentembodiment, selection of the lens surface to which the aspheric sphereis to apply is properly specified so that, without having to influencethe spherical aberration in the telephoto end, the spherical aberrationin the neighborhood of the start point of the F drop is well corrected.Thus, good stability of spherical aberration correction is maintainedover the entire zooming range.

Next, the features of numerical examples of the present embodiment aredescribed.

The numerical example 9 shown in FIG. 22 has a zoom ratio of more than18. R1 to R7 form a front part F1 for focusing of a focusing lens unit,and all of them give it a negative refractive power. R8 to R16 form arear focusing lens unit F2 which remains stationary during focusing andzooming and all of them give it a positive refractive power. R1 throughR16 function as a front lens unit F to focus an object point for avariator V. The front lens unit F has a weak positive refractive poweras a whole.

The variator V of R17 to R23 has main contribution to variation of thefocal length and, when zooming from the wide-angle end to the telephotoend, moves toward the image side monotonously, while its magnificationvaries past -1x (unity magnification) on the way. A compensator C of R24to R30 has a positive refractive power and functions mainly to share thevariation of the focal length and to compensate for the image shift withzooming. When zooming from the wide-angle end to the telephoto end, thecompensator C moves toward the object side monotonously, while itsmagnification varies past -1x on the way. SP (R31) stands for a stop. Arelay lens unit of R32 to R45 has the image forming function. R46 andR47 define a glass block equivalent to a color separation prism.

In this numerical example 9, to assure a great increase of the zoomratio, the variator V has an effect of varying 5.31 times themagnification as zooming throughout and, at the same time, thecompensator C also contributes to 3.45 times variation of themagnification.

Also for the aperture ratio to increase, the F-number F_(NO).1 of thefront lens unit is used as an indicator when F_(NO).1 =f1/(ft/F_(NO).t)is defined. This numerical example then gives F_(NO).1 =1.62. With theF-number of the front lens unit when sustained at this value over theentire zooming range, as the F-number F_(NO).3 of the compensator C isdefined by F_(NO).3 =f3/(2×h3m), a large aperture ratio of F_(NO).3=1.03 results.

For these large values of the aperture ratio, the front lens unit takesmeasure for correcting spherical aberration in the wide-angle end. So,the front lens unit is divided into two parts, of which the frontfocusing lens unit F1 is of negative refractive power and the rearfocusing lens unit F2 is of positive refractive power. These lens unitseach are constructed with a plurality of lens elements, so thatspherical aberration is corrected by the technique of sharing.Furthermore, these lens units each include a cemented lens surface topermit use of the technique of diverging spherical aberration. In such amanner, spherical aberration is suppressed from increasing in the frontlens unit.

In general, the compensator C and the variator V are preferably assimple in the construction and arrangement of the constituent lenses andas short in the axial thickness of the block as possible, from the pointof view of minimizing the bulk and size of the entire system of the zoomlens and of saving consumption of electric energy by the drive system.For this reason, it is desired that the compensator has as small anumber of lens elements as possible.

The F-number F_(NO).3 of the compensator C has, on the other hand, to bevery fast as described before. It is, therefore, difficult to correctaberrations of higher order by the compensator C. Particularly in thezooming positions around the F-drop, spherical aberration tends to varyto large extent.

So, in the numerical example 9, the compensator C is constructed with afirst lens of positive power having a convex surface facing the imageside, followed by a doublet whose cemented surface is concave toward theobject side and then by a positive lens having a convex surface facingthe object side. The production of spherical aberration is thussuppressed. In addition, the cemented surface forms a refractive indexdifference Δn between the media on the front and rear sides thereof.Given Δn=0.17, its effect as the diverging surface for sphericalaberration is heightened.

The aspheric sphere is applied to the surface R29 and the condition (8)has its factor getting h3m/h3T=1.25. The aspheric surface is so orientedthat the positive refractive power gets progressively stronger as theheight of incidence of the axial beam increases. To avoid steep changesin the shape of the aspheric surface and correct spherical aberrationwith good efficiency in lower to higher terms, the aspheric coefficientsC and D only are in use, so that chief aberration correction is made onspherical aberration. Such an aspheric surface deviates 6.2 μm at 1.0 ofthe effective diameter.

The numerical example 10 of FIG. 23 has a zoom ratio of 17. Comparedwith the numerical example 9, the lowered amount of the F-number, or theF-drop, is made small, permitting the compensator to reduce the areathrough which the axial light beam passes only in the neighborhood ofthe start point of the F drop. In other words, the value of h3m/h3T ismade small, and the degree of freedom on the design of the front lensunit is reduced. Nonetheless, a small aspheric amount suffices forsuppressing variation of spherical aberration throughout the zoomingrange.

A focusing lens unit comprises a front part F1 of R1 to R6 for focusinghaving a negative refractive power, and a rear part F2 of R7 to R15having a positive refractive power and stationary during focusing andzooming. The focusing lens unit of R1 to R15 functions as a front lensunit and has a weak positive refractive power.

A variator V of R16 to R22 has a main contribution to variation of thefocal length and, when zooming from the wide-angle end to the telephotoend, moves toward the image side monotonously, while its magnificationvaries past -1x (unity magnification) on the way. A compensator C of R23to R29 functions mainly to share the variation of the focal length andto compensate for the image shift and has a positive refractive power.When zooming from the wide-angle end to the telephoto end, it movestoward the object side monotonously, while its magnification varies past-1x on the way. SP (R30) stands for a stop. A relay lens unit R of R31to R44 has the image forming function. R45 and R46 define a glass blockequivalent to a color separation prism.

In the numerical example 10, to assure a great increase of the zoomratio, the variator V has an effect of varying 4.99 times themagnification and the compensator C, too, contributes to 3.41 times thevariation of magnification.

Again, the front lens unit F has an F-number of F_(NO).1 =1.55 and thecompensator C has an F-number of F_(NO).3 =0.99. The aperture ratio isfound larger.

The compensator C in the numerical example 10, similarly to that in thenumerical example 9, comprises a first lens of positive refractive powerhaving a convex surface facing the image side, a doublet whose cementedsurface is concave toward the object side, and a positive lens having aconvex surface facing the object side. By this, production of sphericalaberration is suppressed. Also, the refractive index difference betweenthe media on the front and rear sides of the cemented surface isΔn=0.17. By this, spherical aberration is well corrected.

In this case, to apply an aspheric surface to the compensator C, thesurface R25 is selected, so that h3m/h3T=1.19 is obtained. The asphericsurface is so oriented that the positive refractive power getsprogressively stronger as the height of incidence of the axial lightbeam increases. To produce a larger effect by a smaller aspheric amount,the refracting power of the surface to which the aspheric sphere isapplied is made higher than in the numerical example 9.

Also, because the ratio of h3m/h3T is smaller, the control of sphericalaberration at or near the start point of the F drop is made in view ofexpanding the degree of freedom on the design of the aspheric surfaceand improving the efficiency of the aspheric surface. Of the asphericcoefficients in the before-described equation for the aspheric surface,not only C and D, but also up to E is used to correct it well in up toas higher a term as h¹⁰. In this case the aspheric deviation amounts toabout 2 μm at 1.0 of the height of the surface R25.

In the numerical example 11 of FIG. 24, the zoom lens has so much high arange as the zoom ratio is 44, while nevertheless being as fast as theF-number of F_(NO).t =3.0 in the telephoto end. A front lens unit(focusing lens unit F) of R1 to R8 moves to effect focusing, but remainsstationary during zooming. To reduce secondary spectrum, the front lensunit F includes two or more convex lenses of which, in particular, theAbbe numbers νd exceed 80. Some of them even exceed 95. The front lensunit F as a whole has a weak positive refractive power.

A variator V of R9 to R15 has main contribution to variation of thefocal length and, when zooming from the wide-angle end to the telephotoend, moves toward the image side monotonously, while its magnificationvaries past -1x (unity magnification) on the way. A compensator C of R16to R25 functions mainly to share the variation of the focal length andto compensate for the image shift and has a positive refractive power.When zooming from the wide-angle end to the telephoto end, it movestoward the object side monotonously, while its magnification varies past-1x on the way. SP (R26) stands for a stop. A relay lens unit of R27 toR42 has the image forming function. R43 and R44 define a glass blockequivalent to a color separation prism.

In the numerical example 11, to assure a great increase of the apertureratio, the variator V has an effect of varying 9.20 times the focallength and, at the same time, the compensator C, too, contributes to4.78 times variation of the focal length.

Also, in the numerical example 11, the front lens unit F has an F-numberof F_(NO).1 =1.28 and the compensator C has an F-number of F_(NO).3=0.83, being very fast.

To reduce the variation of spherical aberration, a solution is searchedwith a point laid on the compensator C, since it has a fast speed ofF_(NO).3 =0.83.

A first lens in the compensator C is made positive with its convexsurface facing the image side. It is followed by a first doublet whosecemented surface is concave toward the image side, then by a seconddoublet whose cemented surface is concave toward the object side, andthen by a positive lens having a convex surface facing the object side.That is, the compensator is constructed in the symmetric form in itself.In addition, the degree of freedom of design is increased. With the helpof these, production of spherical aberration is suppressed.

Then, the second cemented surface is made up with the refractive indexdifference Δn between the media on the front and rear sides thereofbeing increased to Δn=0.23. Its effect as the diverging surface forspherical aberration is thus increased. To achieve achromatism withinthe compensator, the second doublet lens may only be used by largelydifferentiating the Abbe numbers νd of its constituent lenses from eachother. But, the use of the second doublet lens alone would result in atight curvature of its cemented surface, which in turn gives adverseinfluence even to spherical aberration. Therefore, the first doubletlens also is made to share the achromatism of the compensator C. Thus,aberrations are reduced in good balance in the compensator C.

In the numerical example 11, the aspheric sphere is applied to thesurface R24. Since, in this example, h3m/h3T=1.5, because the areathrough which the axial light beam passes only when around the startpoint of F drop, is wider than in the other numerical examples, itbecomes easy to bring out the effect of the aspheric surface. For thisreason, the aspheric sphere for the surface R24 in a very simple formbecomes able to correct aberrations. By virtue of this, of the asphericcoefficients in the equation for the aspheric surface, only D is in use.With such a very low degree of freedom, various aberrations arecontrolled. In this case, the aspheric amount is about 27 μm at 1.0 ofthe effective diameter of the surface R24.

FIG. 31 is a block diagram of a numerical example 12 of a zoom lens ofthe invention in the wide-angle end.

In FIG. 31, a first or focusing lens unit F (front lens unit) ofpositive refractive power is comprised of a front focusing lens unit F1of negative refractive power and a rear focusing lens unit F2 ofpositive refractive power. As the object distance varies, focusing isperformed by moving the front focusing lens unit F1 on an optical axis.

A second lens unit for varying the focal length, or variator V, ofnegative refractive power moves axially toward the image sidemonotonously to effect zooming from the wide-angle end to the telephotoend. A compensator C of positive refractive power moves axially towardthe object side non-linearly to compensate for the image shift withzooming. The variator V and the compensator C constitute a zoomingsystem H. The variator V and the compensator C are used under thecondition that when zooming, the magnification varies in a rangeincluding -1x (unity magnification). SP (R31) stands for a stop, and Rstands for a relay lens unit of positive refractive power. G denotes acolor separation prism or an optical filter, though, in FIG. 31, shownas a glass block.

In the numerical example 12, as in application to such a form of zoomlens, or the so-called 4-unit one, an aspheric sphere of certainfiguring is employed in at least one of lens surfaces in the entiresystem of the zoom lens which satisfies the condition (9) describedbefore. This enables a great increase of the aperture ratio and a greatincrease to be achieved in such a manner that astigmatism, fieldcurvature and spherical aberration are well corrected for high opticalperformance throughout the entire zooming range.

In the numerical example 12, on consideration of the ratio of theincident heights hW and hM falling in the range given by the condition(9), the aspheric sphere is applied to the 17th lens surface R17.Astigmatism is then under-corrected in the wide-angle end (for a focallength of 12.2). Thus, the range of variation of astigmatism withzooming in a region between the focal lengths fw and fM is reduced. Bythe following stage or relay lens system, all aberrations are thencorrected in good balance throughout the entire zooming range.

In general, the zoom lens has its image quality in the marginal zone ofthe full aperture depending largely on variation of, for example,astigmatism and spherical aberration with zooming.

FIGS. 33(A) and 33(B) are diagrams used to explain the typicalvariations with zooming of astigmatism and distortion of the so-called4-unit zoom lens by taking the zooming position in the abscissa.

Now suppose the zoom ratio is Z and the focal length for the wide-angleend is fw. In this case, the astigmatism (meridional image focus) is, asshown in FIG. 33(A), under-corrected with respect to the Gauss imageplane in a region of from the wide-angle end to a zooming position for afocal length fM=fw×Z^(1/4).

As zooming then goes from the zooming position of the focal length fMtoward the telephoto end, the under amount decreases and, at a certainzooming position, changes to the reverse, or over-correction results. Asthe F-number of the entire system varies, the lens system then starts tobe darker in a zooming position (for a focal length fMM). Around thisposition, the over-correction reaches the maximum. After that, whenfurther zooming toward the telephoto end, the over amount decreases,reaching almost zero in the telephoto end (for a focal length ft).

Since the image quality of the marginal zone of the full aperturedepends on astigmatism (field characteristic) and the best image focusof the central zone depends on spherical aberration, it becomesimportant from the standpoint of sustaining good optical performance toharmonize the variations of astigmatism and spherical aberrationthroughout the entire zooming range. If such variations are not madeharmonious, the good optical performance cannot be obtained also overthe entire area of the image frame.

Usually, it is difficult to bring astigmatism and spherical aberrationinto harmony at any station in the entire zooming range.

Meanwhile, as shown in FIG. 33(B), the distortion has a considerablylarge negative value in the wide-angle end (for the focal length fw). Aszooming goes from the wide-angle end (fw) to the telephoto end (ft), thedistortion increases in the plus direction. The zooming then passesthrough a position where the distortion is zero to a position for thefocal length fM where the distortion takes the largest value of plussign. When further zooming from the focal length fM to the telephoto end(ft), the distortion gradually decreases.

Hence, the invention sets forth the condition (9) for selection of atleast one of the lens surfaces to which an aspheric sphere of certainform is to apply. When this condition is satisfied, the range ofvariation of astigmatism and distortion with zooming in a region of fromthe focal length fw in the wide-angle end to the focal length fM isreduced to a minimum.

A solid line curve of FIG. 34(A) reveals that the use of such anaspheric surface improves, among others, astigmatism (meridional imagefocus) for the wide-angle end.

The condition (9) is concerned with the focusing and zooming systems ofthe zoom lens. As these systems include some lenses whose individualeffective diameters are determined depending on part of the entirezooming range, the condition (9), when to introduce an aspheric surface,specifies the one of these lenses which can effect maximum possibleimproved results of suppressing the variation of aberrations due to thefocusing and zooming systems. After the these systems have beencorrected for astigmatism in the wide-angle end by the aspheric surface,the resultant balance of aberrations in the wide-angle end is thenbrought back to a desired one by a suited design of the relay system. Insuch a manner, good stability of astigmatism correction is maintainedthroughout the entire zooming range as shown by a solid line curve inFIG. 34(B).

Meanwhile, in the 4-unit zoom lens, as the focal length varies from theshortest to the longest, the height of incidence of the axial light beamgradually increases. Concerning the spherical aberration in thetelephoto end, it is not always certain that the orientation of theshape of the aspheric surface as determined to correct astigmatism inthe wide-angle end coincides with that which improves sphericalaberration in the telephoto end.

So, in the present embodiment, selection of the lens surface to whichthe aspheric sphere is to apply is limited by the condition in terms ofhW/hT.

In a case where the tendencies of the aspheric surface to improveastigmatism and spherical aberration match each other, however, due tothe property of the aspheric surface, it becomes possible to control theaxial light rays near to the optical axis and the off-axial light rays,when lower aspheric terms are taken into consideration.

If so, the aspheric surface is formed such that in a zone where theon-axial incident height and the off-axial incident height are lowerthan the value hT, the spherical aberration in the telephoto end iscorrected, while in the other zone where these heights are higher thanthe value hT, the astigmatism in the wide-angle end is corrected.

It will be appreciated from the above description that in the presentembodiment, the variation of aberrations produced within the focusingand zooming systems is well corrected not only in themselves but also byusing the relay system. Thus, good stability of optical performance isobtained throughout the entire zooming range.

Next, the numerical data for the examples 9 to 12 of the invention areshown in the following tables for the radius of curvature Ri of the i-thlens surface, when counted from the object side, the i-th axial lensthickness or air separation Di and the refractive index Ni and Abbenumber νi of the glass of the i-th lens element, respectively.

The shape of the aspheric surface is expressed in the coordiates with anX axis in an axial direction and an H axis in the directionperpendicular to an optical axis, the direction in which light advancesbeing taken as positive, by the following equation: ##EQU4## where R isthe radius of the osculating sphere, and A, B, C, D and E are theaspheric coefficients.

    ______________________________________                                        Numerical Example 9                                                           f = 12.2-223.46  Fno = 1:1.6-2.2  2ω = 66.5°-4.2°         ______________________________________                                        R1 = 2455.41                                                                             D1 = 5.40   N1 = 1.69979                                                                              ν1 = 55.5                               R2 = 271.91                                                                              D2 = 28.94                                                         R3 = -267.58                                                                             D3 = 3.00   N2 = 1.69979                                                                              ν2 = 55.5                               R4 = -2503.19                                                                            D4 = 1.98                                                          R5 = 9738.25                                                                             D5 = 3.00   N3 = 1.64254                                                                              ν3 = 60.1                               R6 = 224.83                                                                              D6 = 14.59  N4 = 1.76168                                                                              ν4 = 27.5                               R7 = 1879.70                                                                             D7 = 1.84                                                          R8 = 1282.45                                                                             D8 = 13.52  N5 = 1.62286                                                                              ν5 = 60.3                               R9 = -242.57                                                                             D9 = 0.30                                                          R10 = 1074.61                                                                            D10 = 4.50  N6 = 1.81265                                                                              ν6 = 25.4                               R11 = 150.07                                                                             D11 = 20.80 N7 = 1.48915                                                                              ν7 = 70.2                               R12 = -401.90                                                                            D12 = 0.30                                                         R13 = 160.26                                                                             D13 = 16.10 N7 = 1.48915                                                                              ν8 = 70.2                               R14 = 45982.91                                                                           D14 = 0.30                                                         R15 = 148.13                                                                             D15 = 12.92 N9 = 1.62286                                                                              ν9 = 60.3                               R16 = 512.54                                                                             D16 = Variable                                                     R17 = 95.44                                                                              D17 = 2.40  N10 = 1.77621                                                                             ν10 = 49.6                              R18 = 42.25                                                                              D18 = 9.16                                                         R19 = -1689.53                                                                           D19 = 2.20  N11 = 1.77621                                                                             ν11 = 49.6                              R20 = 84.69                                                                              D20 = 11.71                                                        R21 = -46.36                                                                             D21 = 2.20  N12 = 1.77621                                                                             ν12 = 49.6                              R22 = 779.13                                                                             D22 = 5.58  N13 = 1.93306                                                                             ν13 = 21.3                              R23 = -92.60                                                                             D23 = Variable                                                     R24 = 1110.01                                                                            D24 = 8.90  N14 = 1.48915                                                                             ν14 = 70.2                              R25 = -82.86                                                                             D25 = 0.30                                                         R26 = 325.37                                                                             D26 = 12.18 N15 = 1.64254                                                                             ν15 = 60.1                              R27 = -71.86                                                                             D27 = 2.40  N16 = 1.81265                                                                             ν16 = 25.4                              R28 = -222.32                                                                            D28 = 0.30                                                         R29 = 84.97                                                                              D29 = 9.95  N17 = 1.48915                                                                             ν17 = 70.2                              (Aspheric Surface)                                                            R30 = -1089.44                                                                           D30 = Variable                                                     R31 = (Stop)                                                                             D31 = 5.46                                                         R32 = -50.46                                                                             D32 = 1.40  N18 = 1.65425                                                                             ν18 = 58.5                              R33 = 40.07                                                                              D33 = 5.03  N19 = 1.70443                                                                             ν19 = 30.1                              R34 = 68.80                                                                              D34 = 9.57                                                         R35 = -39.21                                                                             D35 = 1.50  N20 = 1.64254                                                                             ν20 = 60.1                              R36 = -900.35                                                                            D36 = 9.72  N21 = 1.69417                                                                             ν21 = 31.1                              R37 = -37.65                                                                             D37 = 34.00                                                        R38 = 70.67                                                                              D38 = 12.47 N22 = 1.48915                                                                             ν22 = 70.2                              R39 = -90.22                                                                             D39 = 0.20                                                         R40 = -501.75                                                                            D40 = 2.00  N23 = 1.81265                                                                             ν23 = 25.4                              R41 = 57.28                                                                              D41 = 2.70                                                         R42 = 110.58                                                                             D42 = 8.02  N24 = 1.48915                                                                             ν24 = 70.2                              R43 = -75.94                                                                             D43 = 1.10                                                         R44 = 54.30                                                                              D44 = 9.15  N25 = 1.48915                                                                             ν25 = 70.2                              R45 = 1174.57                                                                            D45 = 8.30                                                         R46 = ∞                                                                            D46 = 69.20 N26 = 1.51825                                                                             ν26 = 64.1                              R47 = ∞                                                                 ______________________________________                                        Variable Focal Length                                                         Separation                                                                             12.20    25.38    46.58 162.21 223.46                                ______________________________________                                        D16      1.69     47.69    74.09 108.72 113.29                                D23      171.63   116.40   79.82 17.81  1.12                                  D30      2.00     11.24    21.41 48.80  60.92                                 ______________________________________                                        Shape of Asheric Surface                                                      Osculating Sphere: R = 84.973                                                                       Parameter                                               Aspheric Coefficients Zv = 5.31                                               A = B = E = 0         F.sub.NO.1 = 1.62                                       C = 8.0 × 10.sup.-12                                                                          F.sub.NO.3 = 1.07                                       D = -7.88 × 10.sup.-16                                                                        h3m/h3T = 1.25                                                                Δn = 0.170                                        ______________________________________                                        Aspheric Amount  h       ΔX                                             ______________________________________                                        0.7              (21.56) 0.77 μm                                           0.9              (27.72) 3.35 μm                                           1.0              (30.80) 6.19 μm                                           ______________________________________                                        Numerical Example 10                                                          f = 12.5-212.5  Fno = 1:1.6-2.0  2ω = 65.2°-2.2°          ______________________________________                                        R1 = 671.00                                                                              D1 = 5.40   N1 = 1.69979                                                                              ν1 = 55.5                               R2 = 231.23                                                                              D2 = 29.79                                                         R3 = -209.21                                                                             D3 = 5.009  N2 = 1.64254                                                                              ν2 = 60.1                               R4 = 217.15                                                                              D4 = 0.26                                                          R5 = 215.45                                                                              D5 = 14.51  N3 = 1.76168                                                                              ν3 = 27.5                               R6 = 1673.80                                                                             D6 = 1.84                                                          R7 = 722.69                                                                              D7 = 14.642 N4 = 1.62287                                                                              ν4 = 60.3                               R8 = -239.18                                                                             D8 = 0.30                                                          R9 = 2027.35                                                                             D9 = 4.50   N5 = 1.81265                                                                              ν5 = 25.4                               R10 = 152.60                                                                             D10 = 20.85 N6 = 1.48915                                                                              ν6 = 70.2                               R11 = -370.46                                                                            D11 = 0.30                                                         R12 = 205.51                                                                             D12 = 14.77 N7 = 1.48915                                                                              ν7 = 70.2                               R13 = -1091.03                                                                           D13 = 0.30                                                         R14 = 140.50                                                                             D14 = 14.37 N8 = 1.62287                                                                              ν8 = 60.3                               R15 = 648.10                                                                             D15 = Variable                                                     R16 = 88.91                                                                              D16 = 2.40  N9 = 1.77621                                                                              ν9 = 49.6                               R17 = 41.36                                                                              D17 = 8.20                                                         R18 = -1709.46                                                                           D18 = 2.20  N10 = 1.77621                                                                             ν10 = 49.6                              R19 = 82.40                                                                              D19 = 12.42                                                        R20 = -48.13                                                                             D20 = 2.20  N11 = 1.77621                                                                             ν11 = 49.6                              R21 = 447.27                                                                             D21 = 6.43  N12 = 1.93306                                                                             ν12 = 21.3                              R22 = -100.96                                                                            D22 = Variable                                                     R23 = -3606.86                                                                           D23 = 8.89  N13 = 1.48915                                                                             ν13 = 70.2                              R24 = -82.70                                                                             D24 = 0.30                                                         R25 = 254.65                                                                             D25 = 12.52 N14 = 1.64254                                                                             ν14 = 60.1                              (Aspheric Surface)                                                            R26 = -74.51                                                                             D26 = 2.40  N15 = 1.81265                                                                             ν15 = 25.4                              R27 = -246.12                                                                            D27 = 0.30                                                         R28 = 84.85                                                                              D28 = 10.17 N16 = 1.48915                                                                             ν16 = 70.2                              R29 = -664.23                                                                            D29 = Variable                                                     R30 = (Stop)                                                                             D30 = 5.46                                                         R31 = -51.38                                                                             D31 = 1.40  N17 = 1.65425                                                                             ν17 = 58.5                              R32 = 37.53                                                                              D32 = 4.98  N18 = 1.70443                                                                             ν18 = 30.1                              R33 = 69.05                                                                              D33 = 9.57                                                         R34 = -42.16                                                                             D34 = 1.50  N19 = 1.64254                                                                             ν19 = 60.1                              R35 = -1192.59                                                                           D35 = 8.28  N20 = 1.69417                                                                             ν20 = 30.1                              R36 = -38.86                                                                             D36 = 33.68                                                        R37 = 170.41                                                                             D37 = 12.03 N21 = 1.48915                                                                             ν21 = 70.2                              R38 = -42.17                                                                             D38 = 2.20  N22 = 1.76168                                                                             ν22 = 27.5                              R39 = -54.88                                                                             D39 = 0.20                                                         R40 = 322.72                                                                             D40 = 1.90  N23 = 1.76168                                                                             ν23 = 27.5                              R41 = 40.32                                                                              D41 = 11.53 N24 = 1.51356                                                                             ν24 = 51.0                              R42 = -298.39                                                                            D42 = 1.10                                                         R43 = 59.05                                                                              D43 = 5.64  N25 = 1.48915                                                                             ν25 = 70.2                              R44 = 3002.98                                                                            D44 = 8.30                                                         R45 = ∞                                                                            D45 = 69.20 N26 = 1.51825                                                                             ν26 = 64.2                              R46 = ∞                                                                 ______________________________________                                        Variable Focal Length                                                         Separation                                                                             12.50    22.00    45.30 170.00 212.50                                ______________________________________                                        D15      3.56     40.61    74.13 109.36 113.13                                D22      171.13   127.29   82.45 15.12  3.99                                  D29      2.25     9.05     20.37 52.47  59.82                                 ______________________________________                                        Shape of Asheric Surface                                                      Osculating Sphere: R = 254.65                                                                       Parameter                                               Aspheric Coefficients Zv = 4.99                                               A = B = 0             Zv/Z = 0.3                                              C = 2.534 × 10.sup.-15                                                                        F.sub.NO.1 = 1.55                                       D = -3.133 × 10.sup.-16                                                                       F.sub.NO.3 = 0.99                                       E = 1.845 × 10.sup.-18                                                                        h3m/h3T = 1.19                                                                Δn = 0.17011                                      ______________________________________                                        Aspheric Amount  h       ΔX                                             ______________________________________                                        0.7              (22.61) 0.04 μm                                           0.9              (29.07) 0.65 μm                                           1.0              (32.30) 1.94 μm                                           ______________________________________                                        Numerical Example 11                                                          f = 10.0-440  Fno = 1:1.75-3.0  2ω = 57.6°-0.72°          ______________________________________                                        R1 = 397.20                                                                              D1 = 5.50   N1 = 1.72311                                                                              ν1 = 29.5                               R2 = 182.95                                                                              D2 = 0.70                                                          R3 = 181.76                                                                              D3 = 23.08  N2 = 1.43496                                                                              ν2 = 95.1                               R4 = -601.22                                                                             D4 = 0.30                                                          R5 = 178.22                                                                              D5 = 18.30  N3 = 1.43496                                                                              ν3 = 95.1                               R6 = -4012.90                                                                            D6 = 0.30                                                          R7 = 134.24                                                                              D7 = 11.61  N4 = 1.49845                                                                              ν4 = 81.6                               R8 = 264.84                                                                              D8 = Variable                                                      R9 = 1978.17                                                                             D9 = 2.00   N5 = 1.82017                                                                              ν5 = 46.6                               R10 = 61.00                                                                              D10 = 4.30                                                         R11 = -244.81                                                                            D11 = 1.80  N6 = 1.77621                                                                              ν6 = 49.6                               R12 = 49.97                                                                              D12 = 7.53                                                         R13 = -56.56                                                                             D13 = 1.80  N7 = 1.82017                                                                              ν7 = 46.6                               R14 = 48.78                                                                              D14 = 7.71  N8 = 1.93306                                                                              ν8 = 21.3                               R15 = -227.11                                                                            D15 = Variable                                                     R16 = 1717.21                                                                            D16 = 6.39  N9 = 1.49845                                                                              ν9 = 81.6                               R17 = -106.26                                                                            D17 = 0.30                                                         R18 = 200.29                                                                             D18 = 2.50  N10 = 1.65223                                                                             ν10 = 33.8                              R19 = 72.78                                                                              D19 = 12.98 N11 = 1.59143                                                                             ν11 = 61.2                              R20 = -125.34                                                                            D20 = 0.20                                                         R21 = 107.54                                                                             D21 = 13.87 N12 = 1.62032                                                                             ν12 = 63.4                              R22 = -71.24                                                                             D22 = 2.50  N13 = 1.85501                                                                             ν13 = 23.9                              R23 = -196.04                                                                            D23 = 0.20                                                         R24 = 124.29                                                                             D24 = 3.50  N14 = 1.48915                                                                             ν14 = 70.2                              (Aspheric Surface)                                                            R25 = 221.46                                                                             D25 = Variable                                                     R26 = (stop)                                                                             D26 = 3.29                                                         R27 = -53.23                                                                             D27 = 1.80  N15 = 1.79013                                                                             ν15 = 44.2                              R28 = 36.14                                                                              D28 = 4.09  N16 = 1.81265                                                                             ν16 = 25.4                              R29 = 167.11                                                                             D29 = 5.57                                                         R30 = -34.30                                                                             D30 = 1.60  N17 = 1.73234                                                                             ν17 = 54.7                              R31 = 34.37                                                                              D31 = 10.20 N18 = 1.59911                                                                             ν18 = 39.2                              R32 = -28.89                                                                             D32 = 24.00                                                        R33 = -471.13                                                                            D33 = 5.79  N19 = 1.48915                                                                             ν19 = 70.2                              R34 = -32.79                                                                             D34 = 0.20                                                         R35 = -53.92                                                                             D35 = 2.20  N20 = 1.79013                                                                             ν20 = 44.2                              R36 = 36.97                                                                              D36 = 7.40  N21 = 1.50349                                                                             ν21 = 56.4                              R37 = -66.22                                                                             D37 = 1.10                                                         R38 = 181.90                                                                             D38 = 6.62  N22 = 1.55099                                                                             ν22 = 45.8                              R39 = -30.85                                                                             D39 = 2.20  N23 = 1.81265                                                                             ν23 = 25.4                              R40 = -85.03                                                                             D40 = 0.20                                                         R41 = 73.62                                                                              D41 = 5.14  N24 = 1.51977                                                                             ν24 = 52.4                              R42 = -67.93                                                                             D42 = 5.00                                                         R43 = ∞                                                                            D43 = 50.00 N25 = 1.51825                                                                             ν25 = 64.2                              R44 = ∞                                                                 ______________________________________                                        Variable Focal Length                                                         Separation                                                                             10.00    19.49    69.78 256.60 440.00                                ______________________________________                                        D8       4.53     46.53    94.53 118.03 123.53                                D15      178.14   131.08   68.95 21.77  2.18                                  D25      3.30     8.36     22.49 46.17  60.26                                 ______________________________________                                        Shape of Asheric Surface                                                      Osculating Sphere: R = 124.297                                                                      Parameter                                               Aspheric Coefficients Zv = 9.19                                               A = B = C = E = 0     Zv/Z = 0.209                                            D = 5.997 × 10.sup.-14                                                                        F.sub.NO.1 = 1.28                                                             F.sub.NO.3 = 0.83                                                             h3m/h3T = 1.5                                                                 Δn = 0.228                                        ______________________________________                                        Aspheric Amount  h       ΔX                                             ______________________________________                                        0.7              (20.03) 1.55 μm                                           0.9              (25.75) 11.6 μm                                           1.0              (28.61) 29.6 μm                                           ______________________________________                                        Numerical Example 12                                                          f = 12.2-223.46  Fno = 1:1.6-7.2  2ω = 66.5°-4.2°         ______________________________________                                        R1 = 2455.41                                                                             D1 = 5.40   N1 = 1.69979                                                                              ν1 = 55.5                               R2 = 271.91                                                                              D2 = 28.94                                                         R3 = -267.58                                                                             D3 = 3.009  N2 = 1.69979                                                                              ν2 = 55.5                               R4 = -2503.19                                                                            D4 = 1.98                                                          R5 = 9738.25                                                                             D5 = 3.00   N3 = 1.64254                                                                              ν3 = 60.1                               R6 = 224.83                                                                              D6 = 14.59  N4 = 1.76168                                                                              ν4 = 27.5                               R7 = 1879.70                                                                             D7 = 1.84                                                          R8 = 1282.45                                                                             D8 = 13.52  N5 = 1.62286                                                                              ν5 = 60.3                               R9 = -242.57                                                                             D9 = 0.30                                                          R10 = 1074.61                                                                            D10 = 4.50  N6 = 1.81265                                                                              ν6 = 25.4                               R11 = 150.07                                                                             D11 = 20.80 N7 = 1.48915                                                                              ν7 = 70.2                               R12 = -401.90                                                                            D12 = 0.30                                                         R13 = 160.26                                                                             D13 = 16.10 N8 = 1.48915                                                                              ν8 = 70.2                               R14 = 45982.91                                                                           D14 = 0.30                                                         R15 = 148.13                                                                             D15 = 12.92 N9 = 1.62286                                                                              ν9 = 60.3                               R16 = 512.54                                                                             D16 = Variable                                                     R17 = 95.44                                                                              D17 = 2.40  N10 = 1.77621                                                                             ν10 = 49.6                              (Aspheric Surface)                                                            R18 = 42.25                                                                              D18 = 9.16                                                         R19 = -1689.53                                                                           D19 = 2.20  N11 = 1.77621                                                                             ν11 = 49.6                              R20 = 84.69                                                                              D20 = 11.71                                                        R21 = -46.36                                                                             D21 = 2.20  N12 = 1.77621                                                                             ν12 = 49.6                              R22 = 779.13                                                                             D22 = 5.58  N13 = 1.93306                                                                             ν13 = 21.3                              R23 = -92.60                                                                             D23 = Variable                                                     R24 = 1110.01                                                                            D24 = 8.90  N14 = 1.48915                                                                             ν14 = 70.2                              R25 = -82.86                                                                             D25 = 0.30                                                         R26 = 325.37                                                                             D26 = 12.18 N15 = 1.64254                                                                             ν15 = 60.1                              R27 = -71.86                                                                             D27 = 2.40  N16 = 1.81265                                                                             ν16 = 25.4                              R28 = -222.32                                                                            D28 = 0.30                                                         R29 = 84.97                                                                              D29 = 9.95  N17 = 1.48915                                                                             ν17 = 70.2                              R30 = -1089.44                                                                           D30 = Variable                                                     R31 = (Stop)                                                                             D31 = 5.46                                                         R32 = -50.20                                                                             D32 = 1.40  N18 = 1.65425                                                                             ν18 = 58.5                              R33 = 40.78                                                                              D33 = 4.55  N19 = 1.70443                                                                             ν19 = 30.1                              R34 = 70.60                                                                              D34 = 9.57                                                         R35 = -39.52                                                                             D35 = 1.50  N20 = 1.64254                                                                             ν20 = 60.1                              R36 = -1029.62                                                                           D36 = 9.38  N21 = 1.69417                                                                             ν21 = 31.1                              R37 = -37.67                                                                             D37 = 34.00                                                        R38 = 69.80                                                                              D38 = 12.39 N22 = 1.48915                                                                             ν22 = 70.2                              R39 = -90.33                                                                             D39 = 0.20                                                         R40 = -496.87                                                                            D40 = 2.00  N23 = 1.81265                                                                             ν23 = 25.4                              R41 = 56.71                                                                              D41 = 2.73                                                         R42 = 111.78                                                                             D42 = 7.91  N24 = 1.48915                                                                             ν24 = 70.2                              R43 = -75.35                                                                             D43 = 1.10                                                         R44 = 54.78                                                                              D44 = 8.11  N25 = 1.48915                                                                             ν25 = 70.2                              R45 = 2543.16                                                                            D45 = 8.30                                                         R46 = ∞                                                                            D46 = 69.20 N26 = 1.51825                                                                             ν26 = 64.1                              R47 = ∞                                                                 ______________________________________                                        Variable Focal Length                                                         Separation                                                                             12.20    25.38    46.58 162.21 223.46                                ______________________________________                                        D16      1.69     47.69    74.09 108.72 113.29                                D23      171.63   116.40   79.82 17.81  1.12                                  D30      2.00     11.24    21.41 48.80  60.92                                 ______________________________________                                        Aspheric Surface: R17 Parameter                                               R = 95.446            h.sub.W = 29.05                                         A = 0                 h.sub.M = 20.15                                         B = 0                 h.sub.T = 22.82                                         C = -6.22 × 10.sup.-11                                                  D = 1.5 × 10.sup.-13                                                    E = -7.48 × 10.sup.-17                                                  ______________________________________                                    

According to the invention, the design rules as described above for theso-called 4-unit zoom lens are set forth to determine the ranges ofvariation with zooming of the magnification of the variator andcompensator and the refractive powers and F-numbers of the lens units.As the oblique and axial light beams travel through the lens surfaceswith variation of their heights of incidence, an additional condition isset forth for application of an aspheric sphere to at least one lenssurface. When these conditions are satisfied, the variation of sphericalaberration with zooming is reduced to a minimum and, further, thevariations of astigmatism, field curvature, distortion and otheroff-axial aberrations with zooming are corrected in good balance. Hence,it is made possible to achieve realization of a zoom lens having a largerelative aperture for the wide-angle end of about 1.6 in F-number and ahigh range of 18 to 40 or thereabout, while still maintaining highoptical performance throughout the entire zooming range.

What is claimed is:
 1. A zoom lens comprising, from front to rear, afirst lens unit of positive refractive power stationary during zooming,a second lens unit of negative refractive power for zooming, a thirdlens unit of negative refractive power for compensating for the shift ofan image plane with zooming and a fixed fourth lens unit of positiverefractive power, said zoom lens having a characteristic that theF-number of the entire system starts to increase at an arbitrary stationduring zooming from a wide-angle end to a telephoto end, wherein lettingthe focal length and F-number of said first lens unit be denoted by f1and F_(NO).1, respectively, the lateral magnification for the wide-angleend of said second lens unit by β2w, and the focal length of said secondlens unit and the height of incidence of an axial light beam on the lastlens surface of said second lens unit by f2 and h2m, respectively, saidsecond lens unit being constructed in a form having at least four lenssurfaces and an aspheric surface being applied to at least one lenssurface of the fourth and later lens surfaces of said second lens unit,said aspheric surface satisfying 1.09<hm/ht where hm is the maximumincident height of an axial light beam and ht is the maximum incidentheight of an axial light beam in the telephoto end, and letting theF-number of said second lens unit be denoted by F_(NO).2, the focallength and F-number for the telephoto end of said zoom lens by ft andF_(NO).t, respectively, and the zoom ratio of said zoom lens by Z, andsettingF_(NO).1 =f1/(ft/F_(NO).t) F_(NO).2 =f2/(2×h2m )the followingconditions are satisfied:

    10<Z

    1.01<F.sub.NO.1 <1.65

    0.65<F.sub.NO.2 <1.25

    -0.40<β2w<<-0.15.


2. A zoom lens according to claim 1, wherein said aspheric surface whenapplied to a positive refracting surface is in such form that a positiverefractive power gets progressively stronger toward a marginal zone ofthe lens surface, or when applied to the negative refracting surface, insuch form that a negative refractive power gets progressively weakertoward a marginal zone of the lens surface, and wherein letting theaspheric amounts at 1.0, 0.9 and 0.7 of an effective lens diameter ofsaid aspheric surface be denoted by Δ10, Δ9, and Δ7, respectively, thefollowing conditions are satisfied:

    3.7×10.sup.-5 <|Δ10/f2|<7.7×10.sup.-4

    1.8×10.sup.-5 <|Δ9/f2|<3.8×10.sup.-4

    0<|Δ7/f2|<1.25×10.sup.-4.


3. A zoom lens comprising, from front to rear, a first lens unit ofpositive refractive power stationary during zooming, a second lens unitof negative refractive power for zooming, a third lens unit of negativerefractive power for compensating for the shift of an image plane withzooming and a fixed fourth lens unit of positive refractive power,wherein letting the zoom ratio of said zoom lens be denoted by Z, thefocal length and F-number of said first lens unit by f1 and F_(NO).1,respectively, the lateral magnification for a wide-angle end of saidsecond lens unit by β2w, and the focal length of said second lens unitand the height of incidence of an axial light beam on the last lenssurface of said second lens unit by f2 and h2m, respectively, saidsecond lens unit being constructed in a form having at least four lenssurfaces and an aspheric surface being applied to at least one lenssurface of the fourth and later lens surfaces in said second lens unit,said aspheric surface satisfying 1.17<ht/hz where hz is the maximumincident height of an axial light beam in a zooming position for a zoomratio of Z^(3/4) and ht is the maximum incident height of an axial lightbeam in a telephoto end, and letting the F-number of said second lensunit be denoted by F_(NO).2, and the focal length and F-numbers in thetelephoto and wide-angle ends of said zoom lens by ft, F_(NO).t andF_(NO).w, respectively, and setting

    F.sub.NO.1 =f1/(ft/F.sub.NO.t)

    F.sub.NO.2 =f2/(2×h2m)

    F.sub.NO.R =F.sub.NO.t /F.sub.NO.w

the following conditions are satisfied:

    10<Z

    F.sub.NO.R <1.05

    1.01<F.sub.NO.1 <1.65

    0.65<F<1.28

    -0.40<β2w<-0.16.


4. A zoom lens according to claim 3, wherein said aspheric surface whenapplied to a positive refracting surface is in such form that a positiverefractive power gets progressively weaker toward a marginal zone of thelens surface, or when applied to a negative refracting surface, in suchform that a negative refractive power gets progressively stronger towarda marginal zone of the lens surface, and wherein letting the asphericamounts at 1.0, 0.9 and 0.7 of an effective lens diameter of saidaspheric surface be denoted by Δ10, Δ9 and Δ7, respectively, thefollowing conditions are satisfied:

    3.85×10.sup.-5 <|Δ10/f2|<7×10.sup.-4

    1.95×10.sup.-5 <|Δ9/f2|<3.2×10.sup.-4

    0<|Δ7/f2|<4.7×10.sup.-5.